Rd Sharma 2018 Solutions for Class 8 Math Chapter 9 Linear Equation In One Variable are provided here with simple step-by-step explanations. These solutions for Linear Equation In One Variable are extremely popular among Class 8 students for Math Linear Equation In One Variable Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2018 Book of Class 8 Math Chapter 9 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2018 Solutions. All Rd Sharma 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Page No 9.11:

Question 1:

Solve each of the following equation and also check your result in each case:
2x+53=3x-10

Answer:

2x+53=3x-10or 2x+5=9x-30or 9x-2x=5+30or 7x=35or x=357or x=5Verification:L.H.S.=10+53=153=5R.H.S.=15-10=5 L.H.S.=R.H.S. for x=5.

Page No 9.11:

Question 2:

Solve each of the following equation and also check your result in each case:
a-83=a-32

Answer:

a-83=a-32or 2a-16=3a-9or 3a-2a=-16+9or a=-7 Verification:L.H.S.=-7-83=-153=-5R.H.S.=-7-32=-102=-5

 L.H.S. = R.H.S. for a = -7

Page No 9.11:

Question 3:

Solve each of the following equation and also check your result in each case:
7y+25=6y-511

Answer:

7y+25=6y-511or 77y+22=30y-25or 77y-30y=-25-22or 47y=-47or y=-4747=-1Verification:L.H.S.=-7+25=-55=-1R.H.S.=-6-511=-1111=-1

 L.H.S. = R.H.S. for y = -1

Page No 9.11:

Question 4:

Solve each of the following equation and also check your result in each case:
x-2x+2-163x+5=3-72x

Answer:

x-2x+2-163x+5=3-72xor3x-6x+6-16x+153=6-7x2or-19x+213=6-7x2or -38x+42=18-21xor -21x+38x=42-18or 17x=24or x=2417Check:L.H.S.=2417-2×2417+7-163×2417=-3317R.H.S.=3-72×2417=-3317

 L.H.S. = R.H.S. for x = 2417

Page No 9.11:

Question 5:

Solve each of the following equation and also check your result in each case:
12x+7x-6=7x+14

Answer:

12x+7x-6=7x+14or 12x+7x-7x=14+6orx2=1+244or x2=254or x=252Check:L.H.S.=12×252+7×252-6=3514R.H.S.=7×252+14=3514

 L.H.S. = R.H.S. for x 252

Page No 9.11:

Question 6:

Solve each of the following equation and also check your result in each case:
34x+4x=78+6x-6

Answer:

34x+4x=78+6x-6or 34x-2x=78-6or 3x-8x4=7-488or-5x4=-418or -40x=-164or x=-164-40=4110Check:L.H.S.=34×4110+4×4110=12340+16410=123+65640=77940R.H.S.=78+6×4110-6=78+24610-6=35+984-24040=77940

 L.H.S. = R.H.S. for x4110

Page No 9.11:

Question 7:

Solve each of the following equation and also check your result in each case:
72x-52x=203x+10

Answer:

72x-52x=203x+10or 7x-5x2=20x+303or 40x+60=6xor 34x=-60or x=-6034=-3017Check:L.H.S.=72×-3017-52×-3017=-3017R.H.S.=203×-3017+10=-3017L.H.S.=R.H.S. for x=-3017

Page No 9.11:

Question 8:

Solve each of the following equation and also check your result in each case:
6x+12+1=7x-33

Answer:

6x+12+1=7x-33or 6x+1+22=7x-33or 18x+9=14x-6or 18x-14x=-6-9or 4x=-15or x=-154Check:L.H.S.=6×-154+12+1=-45+2+44=-394R.H.S.=7×-154-33=-105-1212=-394

 L.H.S. = R.H.S. for -154

Page No 9.11:

Question 9:

Solve each of the following equation and also check your result in each case:
3a-23+2a+32=a+76

Answer:

3a-23+2a+32=a+76or 6a-4+6a+96=a+76or 12a+5=6a+7or 6a=7-5or a=26=13Check:L.H.S.=3×13-23+2×13+32=-13+116=96=32R.H.S.=13+76=96=32

 L.H.S. = R.H.S. for 13

Page No 9.11:

Question 10:

Solve each of the following equation and also check your result in each case:
x-(x-1)2=1-(x-2)3

Answer:

x-x-12=1-x-23or 2x-x+12=3-x+23or x+12=5-x3or 3x+3=10-2xor 5x=10-3or x=75Check:L.H.S.=75-75-12=75-15=65R.H.S.=1-75-23=1--315=65

L.H.S. = R.H.S. for 75

Page No 9.11:

Question 11:

Solve each of the following equation and also check your result in each case:
3x4-(x-1)2=(x-2)3

Answer:

3x4-x-12=x-23or 3x-2x+24=x-23or 4x-8=3x+6or x=14Check:L.H.S.=3×144-14-12=212-132=82=4R.H.S.=14-23=123=4

 L.H.S. = R.H.S. for = 14

Page No 9.11:

Question 12:

Solve each of the following equation and also check your result in each case:
5x3-(x-1)4=(x-3)5

Answer:

5x3-x-14=x-35or 20x-3x+312=x-35or 17x+312=x-35or 85x+15=12x-36or 73x=-51or x=-5173Check:L.H.S.=5×-51733--5173-14=-255219--124292=-5473R.H.S.=-5173-35=-5473

 L.H.S. = R.H.S. for -5173

Page No 9.11:

Question 13:

Solve each of the following equation and also check your result in each case:
(3x+1)16+(2x-3)7=(x+3)8+(3x-1)14

Answer:

3x+116+2x-37=x+38+3x-114or 3x+116-x+38=3x-114-2x-37or 3x+1-2x-616=3x-1-4x+614or x-58=-x+57or 7x-35=-8x+40or 15x=75or x=7515=5Check:L.H.S.=3×5+116+2×5-37=1616+77=2R.H.S.=5+38+3×5-114=88+1414=2

 L.H.S. = R.H.S. for = 5

Page No 9.11:

Question 14:

Solve each of the following equation and also check your result in each case:
(1-2x)7-(2-3x)8=32+x4

Answer:

1-2x7-2-3x8=32+x4or 1-2x7=32+x4+2-3x8or 1-2x7=12+2x+2-3x8or 1-2x7=14-x8or 8-16x=98-7xor -16x+7x=98-8or x=-909=-10Check:L.H.S.=1-2×-107-2-3×-108=1+207-2+308=3-4=-1R.H.S.=32+-104=32+-52=3-52=-1

 L.H.S. = R.H.S. for = -10

Page No 9.11:

Question 15:

Solve each of the following equation and also check your result in each case:
9x+72-x-x-27=36

Answer:

9x+72-(x-x-27)=36or 63x+49-14x+2x-414=36or 51x+4514=36or 51x+45=504or 51x=504-45or x=45951=9Thus, x=9 is the solution of the given equation.Check:Substituting x=9 in the given equation, we get:L.H.S.=9×9+72-(9-9-27)=882-9+77=44-9+1=36R.H.S.=36 L.H.S.=R.H.S. for x=9.

Page No 9.11:

Question 16:

Solve each of the following equation and also check your result in each case:
0.18(5x − 4) = 0.5x + 0.8

Answer:

0.18(5x-4)=0.5x+0.8or 0.9x-0.72=0.5x+0.8or 0.9x-0.5x=0.8+0.72or 0.4x=1.52or x=1.520.4or x=3.8Thus, x=3.8 is the solution of the given equation.Check:Substituting x=3.8 in the given equation, we get:L.H.S.=0.18(5×3.8-4)=0.18×15=2.7R.H.S.=0.5×3.8+0.8=2.7 L.H.S.=R.H.S. for x=3.8.

Page No 9.11:

Question 17:

Solve each of the following equation and also check your result in each case:
23x-32x=112

Answer:

23x-32x=112or 4-96x=112or -56x=112or 6x=-60or x=-606or x=-10Thus, x=-10 is the solution of the given equation.Check:Substituting x=-10 in the given equation, we get:L.H.S.=23×(-10)-32×(-10)=2-30-3-20=-4+960=560=112R.H.S.=112 L.H.S.=R.H.S. for x=-10.

Page No 9.11:

Question 18:

Solve each of the following equation and also check your result in each case:
4x9+13+13108x=8x+1918

Answer:

4x9+13+13108x=8x+1918or 48x+36+13x108=8x+1918or 61x+36108=8x+1918or 61x+36=6(8x+19)  [Multiplying both sides by 108]or 61x+36=48x+114or 61x-48x=114-36or 13x=78or x=7813or x=6Thus, x=6 is the solution of the given equation.Check:Substituting x=6 in the given equation, we get:L.H.S.=4×69+13+13108×6=249+13+1318=48+6+1318=6718R.H.S.=8×6+1918=6718 L.H.S.=R.H.S. for x=6.



Page No 9.12:

Question 19:

Solve each of the following equation and also check your result in each case:
(45-2x)15-(4x+10)5=(15-14x)9

Answer:

45-2x15-4x+105=15-14x9or 45-2x-12x-3015=15-14x9or 15-14x5=15-14x3 [Multiplying both sides by 3]or 45-42x=75-70x  [After cross multiplication]or 70x-42x=75-45or 28x=30or x=3028or x=1514Thus, x=1514 is the solution of the given equation.Check:Substituting x=1514 in the given equation, we get:L.H.S.=45-2×151415-4×1514+105=45×7-15105-30+7035=300105-10035=0R.H.S.=15-14×15149=0 L.H.S.=R.H.S. for x=1514

Page No 9.12:

Question 20:

Solve each of the following equation and also check your result in each case:
57x+53-233=13-4x-23

Answer:

5(7x+53)-233=13-4x-23or 35x+253+4x-23=13+233or 35x+25+4x-23=39+233 or 39x+23=62 [Multiplying both sides by 3]or 39x=62-23or x=3939or x=1Thus, x=1 is the solution of the given equation.Check:Substituting x=1 in the given equation, we get:L.H.S.=5(7×1+53)-233=603-233=373R.H.S.=13-4×1-23=39-23=373 L.H.S.=R.H.S. for x=1.

Page No 9.12:

Question 21:

Solve each of the following equation and also check your result in each case:
7x-14-132x-1-x2=103

Answer:

7x-14-13(2x-1-x2)=103or 7x-14-2x3+1-x6=103or 21x-3-8x+2-2x12=103or 11x-1=40  [Multiplying both sides by 12]or 11x=40+1or x=4111Thus, x=4111 is the solution of the given equation.Check:Substituting x=4111 in the given equation, we get:L.H.S.=7×4111-14-13(2×4111-1-41112)=27644-8233+-3066=103R.H.S.=103 L.H.S.=R.H.S. for x=4111

Page No 9.12:

Question 22:

Solve each of the following equation and also check your result in each case:
0.5(x-0.4)0.35-0.6(x-2.71)0.42=x+6.1

Answer:

0.5(x-0.4)0.35-0.6(x-2.71)0.42=x+6.1or (x-0.4)0.7-(x-2.71)0.7=x+6.1orx-0.4-x+2.710.7=x+6.1or -0.4+2.71=0.7x+4.27or 0.7x=2.71-0.4-4.27or x=-1.960.7=-2.8Thus, x=-2.8 is the solution of the given equation.Check:Substituting x=-2.8 in the given equation, we get:L.H.S.=0.5(-2.8-0.4)0.35-0.6(-2.8-2.71)0.42=-1.60.35+3.3060.42=-4.571+7.871=3.3R.H.S.=-2.8+6.1=-3.3 L.H.S.=R.H.S. for x=-2.8

Page No 9.12:

Question 23:

Solve each of the following equation and also check your result in each case:
6.5x+19.5x-32.52=6.5x+13+13x-262

Answer:

6.5x+19.5x-32.52=6.5x+13+13x-262or 19.5x-32.52-13x-262=13or 19.5x-32.5-13x+262=13or 6.5x-6.5=26 [After cross multiplication]or 6.5x=26+6.5or x=32.56.5=5Thus, x=5 is the solution of the given equation.Check:Substituting x=5 in the given equation, we get:L.H.S.=6.5×5+19.5×5-32.52=65R.H.S.=6.5×5+13+13×5-262=65 L.H.S.=R.H.S. for x=5.

Page No 9.12:

Question 24:

Solve each of the following equation and also check your result in each case:
(3x − 8)(3x + 2) − (4x − 11)(2x + 1) = (x − 3)(x + 7)

Answer:

(3x-8)(3x+2)-(4x-11)(2x+1)=(x-3)(x+7)or 9x2+6x-24x-16-8x2-4x+22x+11=x2+7x-3x-21or x2-5=x2+4x-21or 4x=-5+21or x=164=4Thus, x=4 is the solution of the given equation.Check:Substituting x=4 in the given equation, we get:L.H.S.=(3×4-8)(3×4+2)-(4×4-11)(2×4+1)=4×14-5×9=11R.H.S.=(4-3)(4+7)=11 L.H.S.=R.H.S. for x=4.

Page No 9.12:

Question 25:

Solve each of the following equation and also check your result in each case:
[(2x + 3) + (x + 5)]2 + [(2x + 3) − (x + 5)]2 = 10x2 + 92

Answer:

[(2x+3)+(x+5)]2+[(2x+3)-(x+5)]2=10x2+92or (3x+8)2+(x-2)2=10x2+92or 9x2+48x+64+x2-4x+4=10x2+92           [ (a+b)2=a2+b2+2ab  and (a-b)2=a2+b2-2ab ]or 10x2-10x2+44x=92-68or x=2444or x=611Thus, x=611 is the solution of the given equation.Check:Substituting x=611 in the given equation, we get:L.H.S.=2×611+3+611+52+2×611+3-611+52             =  4511+61112+4511-61112               =106112+-16112              =11492121R.H.S.=10×6112+92=360121+92=11492121 L.H.S.=R.H.S. for x=611



Page No 9.17:

Question 1:

Solve the following equation and verify your answer:
2x-33x+2=-23

Answer:

2x-33x+2=-23or 6x-9=-6x-4 (After cross multiplication)or 6x+6x=-4+9or x=512 x=512is the solution of the given equation.Check:L.H.S.= 2×512-33×512+2=56-354+2=-136134=-46=-23R.H.S.=-23 L.H.S.=R.H.S. for x=512

Page No 9.17:

Question 2:

Solve the following equation and verify your answer:
2-yy+7=35

Answer:

2-yy+7=35or 10-5y=3y+21 (After cross multiplication)or 3y+5y=10-21or 8y=-11or y=-118 y=-118 is the solution of the given equation.Check:Substituting y=-118 in the given equation, we get:L.H.S.=2--118-118+7=16+11-11+56=2745=35R.H.S.=35 L.H.S.=R.H.S. for y=-118

Page No 9.17:

Question 3:

Solve the following equation and verify your answer:
5x-73x=2

Answer:

5x-73x=2or 6x=5x-7 (After cross multiplication)or 6x-5x=-7or x=-7 x=-7 is the solution of given equation.Check:Substituting x=-7 in the given equation, we get:L.H.S=5×(-7)-7.3(-7)=-35-7-21=-42-21=2R.H.S.=2 L.H.S.=R.H.S. for x=-7.

Page No 9.17:

Question 4:

Solve the following equation and verify your answer:
3x+52x+7=4

Answer:

3x+52x+7=4or 3x+5=8x+28or 8x+28=3x+5 (After cross multiplication)or8x-3x=5-28or 5x=-23or x=-235 x=-235 is the solution of given equation.Check:Substituting x=-235 in the given equation, we get:L.H.S.=3×-235+52×-235+7=-69+25-46+35=-44-11=4R.H.S.=4 L.H.S.=R.H.S. for x=-235

Page No 9.17:

Question 5:

Solve the following equation and verify your answer:
2y+5y+4=1

Answer:

2y+5y+4=1or 2y+5=y+4or 2y-y=4-5or y=-1Thus, y=-1 is the solution of the given equation.Check:Substituting y=-1 in the given equation, we get:L.H.S.=2(-1)+5-1+4=-2+53=33=1R.H.S.=1 L.H.S.=R.H.S. for y=-1.

Page No 9.17:

Question 6:

Solve the following equation and verify your answer:
2x+13x-2=59

Answer:

2x+13x-2=59or 18x+9=15x-10 [After cross multiplication]or 18x-15x=-10-9or 3x=-19or x=-193Thus, x=-193 is the solution of the given equation.Check:Substituting x=-193 in the given equation, we get:L.H.S.=2(-193)+13(-193)-2=-38+3-57-6=-35-63=59R.H.S.=59 L.H.S.=R.H.S. for x=-193

Page No 9.17:

Question 7:

Solve the following equation and verify your answer:
1-9y19-3y=58

Answer:

1-9y19-3y=58or 8-72y=95-15y  [After cross multiplication]or 95-15y=8-72y  or 72y-15y=8-95or 57y=-87or y=-8757or y=-2919Thus y=-2919 is the solution of the given equation.Check:Substituting y=-2919 in the given equation, we get:L.H.S.=1-9(-2919)19-3(-2919)=19+261361+87=280448=58R.H.S.=58 L.H.S.=R.H.S. for y=-2919

Page No 9.17:

Question 8:

Solve the following equation and verify your answer:
2x3x+1=-3

Answer:

2x3x+1=-3or 2x=-9x-3  [After cross multiplication]or 2x+9x=-3or 11x=-3or x=-311Thus, x=-311 is the solution of the given equation.Check:Substituting x=-311 in the given equation, we get:L.H.S.=2(-311)3(-311)+1=-6-9+11=-62=-3R.H.S.=-3 L.H.S.=R.H.S. for x=-311

Page No 9.17:

Question 9:

Solve the following equation and verify your answer:
y-(7-8y)9y-(3+4y)=23

Answer:

y-(7-8y)9y-(3+4y)=23or 9y-75y-3=23or 27y-21=10y-6  [After cross multiplication]or 27y-10y=-6+21or 17y=15or y=1517Thus, y=1517 is the solution of the given equation.Check:Substituting y=1517 in the given equation, we get:L.H.S.=9(1517)-75(1517)-3=135-11975-51=1624=23R.H.S.=23 L.H.S.=R.H.S. for y=1517

Page No 9.17:

Question 10:

Solve the following equation and verify your answer:
62x-(3-4x)=23

Answer:

62x-(3-4x)=23or 66x-3=23or 12x-6=18   [After cross multiplication]or 12x=18+6or x=2412or x=2Thus, x=2 is the solution of the given equation.Check:Substituting x=2 in the given equation, we get:L.H.S.=62×2-(3-4×2)=69=23R.H.S.=23 L.H.S.=R.H.S. for x=2.

Page No 9.17:

Question 11:

Solve the following equation and verify your answer:
23x-32x=112

Answer:

23x-32x=112or, 4-96x=112or, -5x=12or, x=-10  [After cross multiplication]Thus, x=-10 is the solution of the given equation.Check:Substituting x=-10 in the given equation, we get:L.H.S.=23(-10)-32(-10)=2-30-3-20=4-9-60=-5-60=112R.H.S.=112 L.H.S.=R.H.S. for x=-10.

Page No 9.17:

Question 12:

Solve the following equation and verify your answer:
3x+54x+2=3x+44x+7

Answer:

3x+54x+2=3x+44x+7or, 12x2+20x+21x+35=12x2+16x+6x+8   [Cross multiply]or, 12x2-12x2+41x-22x=8-35or, 19x=-27or, x=-2719Thus, x=-2719 is the solution of the given equationCheck:Substituting x=-2719 in the given equation, we get:L.H.S.=3(-2719)+54(-2719)+2=-81+95-108+38=14-70=-15R.H.S.=3(-2719)+44(-2719)+7=-81+76-108+133=-525=-15 L.H.S.=R.H.S. for x=-2719

Page No 9.17:

Question 13:

Solve the following equation and verify your answer:
7x-25x-1=7x+35x+4

Answer:

7x-25x-1=7x+35x+4or 35x2+28x-10x-8=35x2+15x-7x-3  [After cross multiplication]or 35x2-35x2+18x-8x=-3+8or 10x=5or x=510or x=12Thus, x=12 is the solution of the given equation.Check:Substituting x=12 in the given equation, we get:L.H.S.=7(12)-25(12)-1=7-45-2=33=1R.H.S.=7(12)+35(12)+4=7+65+8=1313=1 L.H.S.=R.H.S. for x=12

Page No 9.17:

Question 14:

Solve the following equation and verify your answer:
x+1x+22=x+2x+4

Answer:

x+1x+22=x+2x+4or x2+2x+1x2+4x+4=x+2x+4or x3+2x2+x+4x2+8x+4=x3+4x2+4x+2x2+8x+8  [After cross multiplication]or x3-x3+6x2-6x2+9x-12x=8-4or -3x=4or x=4-3=-43Thus, x=-43 is the solution of the given equation.Check:Substituting x=-43 in the given equation, we get:L.H.S.=-43+1-43+22=-4+3-4+62=14R.H.S.=-43+2-43+4=-4+6-4+12=28=14 L.H.S.=R.H.S. for x=-43

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Question 15:

Solve the following equation and verify your answer:
x+1x-42=x+8x-2

Answer:

x+1x-42=x+8x-2or x2+2x+1x2-8x+16=x+8x-2       [(a+b)2=a2+b2+2ab  and  (a-b)2=a2+b2-2ab ]or x3+2x2+x-2x2-4x-2=x3-8x2+16x+8x2-64x+128  [After cross multiplication]or x3-x3-3x+48x=128+2or 45x=130or x=13045=269Thus x=269 is the solution of the given equation.Check:Substituting x=269 in the given equation, we get:L.H.S.=269+1269-42=26+926-362=1225100=494R.H.S.=269+8269-2=26+7226-18=988=494 L.H.S.=R.H.S. for x=269

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Question 16:

Solve the following equation and verify your answer:
9x-73x+5=3x-4x+6

Answer:

9x-73x+5=3x-4x+6or 9x2-7x+54x-42=9x2-12x+15x-20  [After cross multiplication]or 9x2-9x2+47x-3x=-20+42or 44x=22or x=2244or x=12Thus, x=12 is the solution of the given equation.Check:Substituting x=12 in the given equation, we get:L.H.S.=9(12)-73(12)+5=9-143+10=-513R.H.S.=3(12)-412+6=3-81+12=-513 L.H.S.=R.H.S. for x=12

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Question 17:

Solve the following equation and verify your answer:
x+2x+5=xx+6

Answer:

x+2x+5=xx+6or x2+2x+6x+12=x2+5x  [After cross multiplication]or x2-x2+8x-5x=-12or 3x=-12or x=-123or x=-4Thus, x=-4 is the solution of given equation.Check:Substituting x=-4 in the given equation, we get:L.H.S.=-4+2-4+5=-2R.H.S.=-4-4+6=-2 L.H.S.=R.H.S. for x=-4.

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Question 18:

Solve the following equation and verify your answer:
2x-(7-5x)9x-(3+4x)=76

Answer:

2x-(7-5x)9x-(3+4x)=76or 7x-75x-3=76or 42x-42=35x-21  [After cross multiplication]or 42x-35x=-21+42or 7x=21or x=217or x=3Thus, x=3 is the solution of the given equation.Check:Substituting x=3 in the given equation, we get:L.H.S.=2×3-(7-5×3)9×3-(3+4×3)=6-(7-15)27-(3+12)=6+827-15=1412=76R.H.S.=76 L.H.S.=R.H.S. for x=3.

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Question 19:

Solve the following equation and verify your answer:
15(2-x)-5(x+6)1-3x=10

Answer:

15(2-x)-5(x+6)1-3x=10or 30-15x-5x-301-3x=10or -20x1-3x=10or 10-30x=-20x  [After cross multiplication]or -20x+30x=10or 10x=10or x=1Thus, x=1 is the solution of the given equation.Check:Substituting x=1 in the given equation, we get:L.H.S.=15(2-1)-5(1+6)1-3(1)=15-35-2=-20-2=10R.H.S.=10 L.H.S.=R.H.S. for x=1.

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Question 20:

Solve the following equation and verify your answer:
x+3x-3+x+2x-2=2

Answer:

x+3x-3+x+2x-2=2or x+3x-3=2-x+2x-2or x+3x-3=2x-4-x-2x-2or x+3x-3=x-6x-2or x2-2x+3x-6=x2-3x-6x+18  [After cross multiplication]or x2-x2+x+9x=18+6or 10x=24or x=2410or x=125Thus, x=125 is the solution of the given equation.Check:Substituting x=125 in the given equation, we get:L.H.S.=125+3125-3+125+2125-2=12+1512-15+12+1012-10=27-3+222=54-66-6=-12-6=2R.H.S.=2 L.H.S.=R.H.S. for x=125

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Question 21:

Solve the following equation and verify your answer:
(x+2)(2x-3)-2x2+6x-5=2

Answer:

(x+2)(2x-3)-2x2+6x-5=2or 2x2+x-6-2x2+6x-5=2or xx-5=2or 2x-10=x  [After cross multiplication]or 2x-x=10or x=10Thus, x=10 is the solution of the given equation.Check:Substituting x=10 in the given equation, we get:L.H.S.=(10+2)(2×10-3)-2×102+610-5=12×17-200+65=105=2R.H.S.=2 L.H.S.=R.H.S. for x=10.

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Question 22:

Solve the following equation and verify your answer:
x2-(x+1)(x+2)5x+1=6

Answer:

x2-(x+1)(x+2)5x+1=6or x2-x2-2x-x-25x+1=6or -3x-25x+1=6or 30x+6=-3x-2  [After cross multiplication]or 30x+3x=-2-6or 33x=-8 or x=-833Thus, x=-833 is the solution of the given equation.Check:Substituting x=-833 in the given equation, we get:L.H.S.=(-833)2-(-833+1)(-833+2)5(-833)+1=641089-2533×5833-4033+1=641089-14501089-733=-13861089-733=427=R.H.S.=6 L.H.S.=R.H.S. for x=-833

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Question 23:

Solve the following equation and verify your answer:
(2x+3)-(5x-7)6x+11=-83

Answer:

(2x+3)-(5x-7)6x+11=-83or -3x+106x+11=-83or -9x+30=-48x-88  [After cross multiplication]or -9x+48x=-88-30or 39x=-118or x=-11839Thus, x=-11839 is the solution of the given equation.Check:Substituting x=-11839 in the given equation, we get:L.H.S.=-3(-11839)+106(-11839)+11=354+390-708+429=744-279=-8-3R.H.S.=-83 L.H.S.=R.H.S. for x=-11839

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Question 24:

Find a positive value of x for which the given equation is satisfied:
(i) x2-95+x2=-59
(ii) y2+43y2+7=12

Answer:

(i) x2-95+x2=-59or 9x2-81=-25-5x2  [After cross multiplication]or 9x2+5x2=-25+81or 14x2=56or x2=5614or x2=4=22or x=2Thus, x=2 is the solution of the given equation.Check:Substituting x=2 in the given equation, we get:L.H.S.=22-95+22=4-95+4=-59R.H.S.=-59 L.H.S.=R.H.S. for x=2.(ii) y2+43y2+7=12or 3y2+7=2y2+8  [After cross multiplication]or 3y2-2y2=8-7or y2=1or y=1Thus, y=1 is the solution of the given equation.Check:Substituting y=1 in the given equation, we get:L.H.S.=12+43(1)2+7=510=12R.H.S.=12 L.H.S.=R.H.S. for y=1.



Page No 9.29:

Question 1:

Four-fifth of a number is more than three-fourth of the number by 4. Find the number.

Answer:

Let the number be x.According to the question, 45x-34x=4or 16x-15x20=4or x=80  [After cross multiplication]Thus, the required number is 80.

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Question 2:

The difference between the squares of two consecutive numbers is 31. Find the numbers.

Answer:

Let the numbers be x and x+1.According to the question,(x + 1)2 - x2 = 31or x2 + 2x + 1 - x2 = 31or 2x = 31 - 1or x = 302or x = 15Thus, the numbers are 15 and 16.

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Question 3:

Find a number whose double is 45 greater than its half.

Answer:

Let the number be x.According to the question,2x = 12x + 45or 2x - 12x = 45or 4x-x2 = 45or 3x = 90 [After cross multiplication]or x = 903or x = 30Thus, the number is 30.

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Question 4:

Find a number such that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.

Answer:

Let the number be x.According to the question,5x - 5 = 2x + 4or 5x - 2x = 4 + 5or 3x = 9or x = 93or x =  3Thus, the number is 3.

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Question 5:

A number whose fifth part increased by 5 is equal to its fourth part diminished by 5. Find the number.

Answer:

Let the number be x.According to the question,x5 + 5 = x4 - 5or x5 - x4 = -5 - 5or 4x-5x20 = -10or -x = -200 [After cross multiplication]or x = 200Thus, the number is 200.

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Question 6:

A number consists of two digits whose sum is 9. If 27 is subtracted from the number, its digits are reversed. Find the number.

Answer:

Let the units digit be x. Sum of two digits = 9 Tens digit = (9-x) Original number =10×(9-x)+x     Reversed number = 10x+(9-x)According to the question,10×(9-x)+x-27 = 10x+(9-x)or 90-10x+x-27 = 10x+9-xor 9x+9x = 90-27-9or 18x = 54or x = 5418 = 3 The number =10×(9-3)+3 = 63

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Question 7:

Divide 184 into two parts such that one-third of one part may exceed one-seventh of another part by 8.

Answer:

Let the first part of 184 be x.Therefore, the other part will be (184-x).According to the question,13x-17(184-x) = 8or 7x-552+3x21 = 8or 10x-552 = 168 [After cross multiplication]or 10x = 168+552or x = 72010 = 72Thus, the parts of 184 are 72 and 112 (184-72 = 112).

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Question 8:

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction is equal to 23. What is the original fraction equal to?

Answer:

Let the denominator of the fraction be x.Therefore, the numerator will be ( x-6). Fraction = x-6xAccording to the question,x-6+3x = 23or x-3x = 23or 3x-9 = 2x [After cross multiplication]or 3x-2x = 9or x = 9Thus, the original fraction = 9-69=13

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Question 9:

A sum of Rs 800 is in the form of denominations of Rs 10 and Rs 20. If the total number of notes be 50, find the number of notes of each type.

Answer:

Let the number of Rs. 10 notes be x.Therefore, the number of Rs. 20 notes will be (50-x).Value of Rs. 10 notes = 10xValue of Rs. 20 notes = 20(50-x)According to the question,10x+20(50-x) = 800or 10x+1000-20x = 800or 10x = 1000-800or x = 20010 = 20 Number of Rs. 10 notes = 20     Number of Rs. 20 notes = (50-20) = 30. 

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Question 10:

Seeta Devi has Rs 9 in fifty-paise and twenty five-paise coins. She has twice as many twenty-five paise coins as she has fifty-paise coins. How many coins of each kind does she have?

Answer:

Let the number of 50 paise coins be x.Therefore, the number of 25 paise coins will be 2x.Value of 50 paise coins = Rs. 0.5xValue of 25 paise coins = Rs. 0.25×2xAccording to the question,0.5x+0.25×2x = 9or x = 9 Number of fifty paise coins = 9     Number of twenty five paise coins = 2×9 = 18     Total number of coins = 9+18 = 27.



Page No 9.30:

Question 11:

Sunita is twice as old as Ashima. If six years is subtracted from Ashima's age and four years added to Sunita's age, then Sunita will be four times Ashima's age. How old were they two years ago?

Answer:

Let the age of Ashima be x years.Therefore, the age of Sunita will be 2x years.According to the question,4(x-6) = 2x+4or 4x-24 = 2x+4or 4x-2x = 4+24or 2x = 28or x = 14 Age of Ashima = 14 years.     Age of Sunita = 2×14 = 28 years.

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Question 12:

The ages of sonu and Monu are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

Answer:

It is given that the ratio of the ages of Sonu and Monu is 7:5.Let the present ages of Sonu and Monu be 7x and 5x years.After ten years:Age of Sonu = 7x + 10 years Age of Monu = 5x + 10 yearsAccording to the question,7x + 105x + 10 = 97or 49x + 70 = 45x + 90or 49x - 45x = 90 - 70or 4x = 20or x = 5 Present age of Sonu = 7 × 5 = 35 years.    Present age of Monu = 5 × 5 = 25 years.

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Question 13:

Five years ago a man was seven times as old as his son. Five years hence, the father will be three times as old as his son. Find their present ages.

Answer:

Five years ago:Let the age of the son be x years.Therefore, the age of the father will be 7x years. Present age of the son = (x + 5) years     Present age of the father = (7x + 5) yearsAfter five years:Age of the son = (x + 5 + 5) = (x + 10) yearsAge of the father = (7x + 5 + 5) = (7x + 10) yearsAccording to the question,7x + 10 = 3(x + 10)or 7x - 3x = 30 - 10or 4x = 20or x = 5 Present age of the son = (5 + 5) = 10 years.     Present age of the father = (7 × 5 + 5) = 40 years.

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Question 14:

I am currently 5 times as old as my son. In 6 years time I will be three times as old as he will be then. What are our ages now?

Answer:

Let the age of my son be x years.Therefore, my age will be 5x years.After 6 years:Age of my son = (x + 6) yearsMy age = (5x + 6) yearsAccording to the question,5x + 6 = 3(x + 6)or 5x - 3x = 18 - 6or 2x = 12or x = 6 Age of my son = 6 years.     My age = 5 × 6 = 30 years.

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Question 15:

I have Rs 1000 in ten and five rupee notes. If the number of ten rupee notes that I have is ten more than the number of five rupee notes, how many notes do I have in each denomination?

Answer:

Let the number of five-rupee notes be x.Therefore, the number of ten-rupee notes will be (x+10).Now,Value of five-rupee notes = Rs. 5xValue of ten-rupee notes = Rs. 10(x + 10)According to the question,5x + 10(x + 10) = 1000or 15x = 1000 - 100or x = 90015 = 60 Number of five-rupee notes = 60.     Number of ten-rupee notes = 60 + 10 = 70. 

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Question 16:

At a party, colas, squash and fruit juice were offered to guests. A fourth of the guests drank colas, a third drank squash, two fifths drank fruit juice and just three did not drink any thing. How many guests were in all?

Answer:

Let the total number of guests be x.Therefore, the number of guests, who drank colas, would be 14x.The number of guests, who drank squash, would be 13x.The number of guests, who drank fruit juice, would be 25x.The number of guests, who did not drink, would be 3.According to the question,x - (x4 + x3 + 2x5) = 3or 60x - 15x - 20x - 24x60 = 3or x = 180Thus, total number of guests =180.

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Question 17:

There are 180 multiple choice questions in a test. If a candidate gets 4 marks for every correct answer and for every unattempted or wrongly answered question one mark is deducted from the total score of correct answers. If a candidate scored 450 marks in the test, how many questions did he answer correctly?

Answer:

Let the number of correctly answered questions be x.Therefore, the number of unattempted or wrongly answered questions will be (180 - x).According to the question,4x - 1(180 - x) = 450or 5x = 450 + 180or x = 6305 = 126Thus, number of correctly answered questions =126.Number of unattempted or wrongly answered questions =180 - 126 = 54.

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Question 18:

A labourer is engaged for 20 days on the condition that he will receive Rs 60 for each day, he works and he will be fined Rs 5 for each day, he is absent. If he receives Rs 745 in all, for how many days he remained absent?

Answer:

Let the number of days for which the labourer is absent be x.Therefore, the number of days for which he is present will be (20-x). Earnings = Rs. 60(20 - x)     Fine = Rs. 5xAccording to the question,60(20 - x) - 5x = 745or 1200 - 60x - 5x = 745or 65x = 1200 - 745or x = 45565 = 7Thus, the labourer was absent for 7 days.

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Question 19:

Ravish has three boxes whose total weight is 6012 kg. Box B weighs 312 kg more than box A and box C weighs 513 kg more than box B. Find the weight of box A.

Answer:

Let the weight of box A be x kg.Therefore, the weights of box B and box C will be (x + 312) kg and (x + 312 + 513) kg, respectively.According to the question,x + (x + 312) + (x + 312 + 513) = 6012or 3x = 1212 - 72 - 72 - 163or 3x = 363 - 21 - 21 - 326or 3x = 2896or x = 28918Thus, weight of box A = 28918 kg

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Question 20:

The numerator of a rational number is 3 less than the denominator. If the denominator is increased by 5 and the numerator by 2, we get the rational number 1/2.  Find the rational number.

Answer:

Let, the denominator of the rational number be x. The numerator of the rational number will be x-3. The rational number =x-3xAccording to the question,x - 3 + 2x + 5 = 12or x - 1x + 5 = 12or 2x - 2 = x + 5or 2x - x = 5 + 2or x = 7 The rational number = 7 - 37 = 47

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Question 21:

In a rational number, twice the numerator is 2 more than the denominator. If 3 is added to each, the numerator and the denominator, the new fraction is 2/3. Find the original number.

Answer:

Let the denominator be x. The numerator = x + 22 The rational number = x + 22xAccording to the question,x + 22 + 3x + 3 = 23or x + 2 +  62(x + 3) = 23or x + 82x + 6 = 23or 3x +  24 = 4x + 12or x = 24 - 12or x = 12The rational number=12 + 22 × 12 = 1424 = 712

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Question 22:

The distance between two stations is 340 km. Two trains start simultaneously from these stations on parallel tracks to cross each other. The speed of one of them is greater than that of the other by 5 km/hr. If the distance between the two trains after 2 hours of their start is 30 km, find the speed of each train.

Answer:

Let, the speed of the first train be x km/h.Then, the speed of the other train will be (x + 5) km/h.2 hours after they started:Distance of the first train from the starting point = 2x kmDistance of the other train from the starting point = 2(x + 5) kmNow,2(x + 5) + 2x + 30 = 340or 4x + 10 + 30 = 340or 4x = 340 - 40or x = 3004 = 75 Speed of the first train = 75 km/h.     Speed of the other train = (75 + 5)=80 km/h.

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Question 23:

A steamer goes downstream from one point to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/hr, find the speed of the steamer in still water and the distance between the ports.

Answer:

It is given that the speed of the stream is 1 km/h.Let the speed of the steamer in still water be x km/h. Downstream speed = (x + 1) km/h     Upstream speed = (x - 1) km/hThe downstream and upstream distances are same; therefore, we have:9(x + 1) = 10(x - 1)or 9x + 9 = 10x - 10or x = 19 Speed of the steamer in still water = 19 km/h.     Distance between the ports = 9(19 + 1) = 180 km.

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Question 24:

Bhagwanti inherited Rs 12000.00. She invested part of it as 10% and the rest at 12%. Her annual income from these investments is Rs 1280.00. How much did she invest at each rate?

Answer:

At the rate of 10%, let the investment by Bhagwanti be Rs. x.Therefore, at the rate of 12%, the investment will be Rs. (12000-x).At the rate of 10%, her annual income = x × 10%At the rate of 12%, her annual income = (12000 - x) × 12%So,x × 0.1 + 0.12(12000 - x) = 1280or 0.1x - 0.12x = 1280 - 1440or 0.02x = 160or x = 8000Thus, at the rate of 10%, she invested Rs. 8000 and at the rate of 12%, she invested Rs. 4000 (12000-8000). 

Page No 9.30:

Question 25:

The length of a rectangle exceeds its breadth by 9 cm. If length and breadth are each increased by 3 cm, the area of the new rectangle will be 84 cm2 more than that of the given rectangle. Find the length and breath of the given rectangle.

Answer:

Let the breadth of the rectangle be x cm.Therefore, the length of the rectangle will be (x + 9) cm. Area of the rectangle = x(x + 9) cm2.If the length and breadth are increased by 3 cm each, area = (x + 3)(x + 9 + 3) cm2.Now,(x + 3)(x + 12) - x(x + 9) = 84or x2 + 15x + 36 - x2 - 9x = 84or 6x = 84 - 36or x = 486 = 8.Thus, breadth of the rectangle = 8 cm.          Length of the rectangle =(8+9)=17 cm.



Page No 9.31:

Question 26:

The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son Anuj is now. Anuj will be eight years older than Anup is now, when Anup is as old as his father. What are their ages now?

Answer:

Let Anup's age be x years.Therefore, his father's age will be (100 - x) years.When Anup is as old as his father after (100 - 2x) years, Anuj's age = 100 - x5 + 100 - 2x years=600 - 11x5 years.Again, when Anup is as old as his father, Anuj's age = x + 8.Now,600 - 11x5 = x + 8or 600 - 11x = 5x + 40or 16x = 560or x = 35.Thus, Anup's age = 35 years          Anup's father's age=100 - x = 100 - 35 = 65 years          Anuj's age = x + 8 = 35 + 8 = 43 years

Page No 9.31:

Question 27:

A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a beggar waiting outside the shop. She spent half of what was left on a lunch and followed that up with a two rupee tip. She spent half of the remaining amount on a book and three rupees on bus fare. When she reached home, she found that she had exactly one rupee left. How much money did she start with?

Answer:

Suppose, the lady started with x rupees.Money spent on shopping=x2 rupeesRemaining amount=x-x2=x2 rupeesAfter giving a rupee she had=(x2-1) rupeesMoney spent on lunch=12(x2-1) rupeesAfter giving a two-rupee tip she had=12(x2-1)-2=x-2-84=x-104 rupeesMoney spent on a book=12(x-104) rupeesAfter spending three rupees on bus fare she had=12(x-104)-3=x-10-248=x-348 rupeesNow,x-348=1or x-34=8or x=42Therefore, she started with 42 rupees.



Page No 9.5:

Question 1:

Solve each of the following equation and also verify your solution:
914=y-113

Answer:

914=y-113or 374+43=y or y=12712  y=12712 for the given equation. Check:L.H.S=914 R.H.S=12712-113=12712-43=127-1612=11112=914 So, L.H.S=R.H.S for y=12712

Page No 9.5:

Question 2:

Solve each of the following equation and also verify your solution:
5x3+25=1

Answer:

5x3+25=1 5x3=1-25 5x3=35 x=35×35=925Verification:L.H.S.=53×925+25=35+2 5=1R.H.S.=1 L.H.S.=R.H.S. for x=925

Page No 9.5:

Question 3:

Solve each of the following equation and also verify your solution:
x2+x3+x4=13

Answer:

x2+x3+x4=13 x×6+x×4+x×312=13 13x12=13 x=13×1213=12Verification:L.H.S.=122+123+124=6+4+3=13=R.H.S.

Page No 9.5:

Question 4:

Solve each of the following equation and also verify your solution:
x2+x8=18

Answer:

x2+x8=18or 4x+x8=18or 5x8=18or x=18×85=15Verification:L.H.S.=12×15+18×15=110+140=540=18=R.H.S.

Page No 9.5:

Question 5:

Solve each of the following equation and also verify your solution:
2x3-3x8=712

Answer:

2x3-3x8=712or 16x-9x24=712or 7x24=712or x=712×247=2Verification:L.H.S.=43-68=32-1824=712R.H.S.=712 R.H.S.=L.H.S. for x=2

Page No 9.5:

Question 6:

Solve each of the following equation and also verify your solution:
(x + 2)(x + 3) + (x − 3)(x − 2) − 2x(x + 1) = 0

Answer:

(x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0or x2+5x+6+x2-5x+6-2x2-2x=0or 12-2x=0or x=122=6Verification:L.H.S.=(6+2)(6+3)+(6-3)(6-2)-2×6(6+1)=72+12-84=0=R.H.S.

Page No 9.5:

Question 7:

Solve each of the following equation and also verify your solution:
x2-45+x5+3x10=15

Answer:

x2-45+x5+3x10=15or x2+x5+3x10=15+45or 5x+2x+3x10=55or 10x10=1or x=1Verification:L.H.S.=12-45+15+310=5-8+2+310=15=R.H.S.

Page No 9.5:

Question 8:

Solve each of the following equation and also verify your solution:
7x+35=110

Answer:

7x+35=110or 7x=110-35or 7x=1-35010or x7=10-349or x=-10×7349=-70349Verification:L.H.S.=7-70349+35=7×349-70+35=349-10+35=110=R.H.S.

Page No 9.5:

Question 9:

Solve each of the following equation and also verify your solution:
2x-13-6x-25=13

Answer:

2x-13-6x-25=13or 10x-5-18x+615=13or -8x+115=13or -24x+3=15or 24x=3-15or x=-1224=-12Verification:L.H.S.=2×-12-13-6×-12-25=-23--55=-2+33=13=R.H.S.

Page No 9.5:

Question 10:

Solve each of the following equation and also verify your solution:
13(y − 4) − 3(y − 9) − 5(y + 4) = 0

Answer:

13(y-4)-3(y-9)-5(y+4)=0or 13y-52-3y+27-5y-20=0or 5y=45or y=455=9Verification:L.H.S.=13(9-4)-3(9-9)-5(9+4)=13×5-3×0-5×13=0=R.H.S.

Page No 9.5:

Question 11:

Solve each of the following equation and also verify your solution:
23(x-5)-14(x-2)=92

Answer:

23(x-5)-14(x-2)=92or 2x-103-x-24=92or 8x-40-3x+612=92or 5x-3412=92or 10x-68=108or 10x=108+68or x=17610=885Verification:L.H.S.=23(885-5)-14(885-2)=23×635-14×785=92=R.H.S.



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