Rs Aggarwal 2019 Solutions for Class 7 Math Chapter 12 Simple Interest are provided here with simple step-by-step explanations. These solutions for Simple Interest are extremely popular among Class 7 students for Math Simple Interest Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2019 Book of Class 7 Math Chapter 12 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2019 Solutions. All Rs Aggarwal 2019 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

Page No 165:

Question 1:

Find the simple interest and the amount when:

Principal = Rs 6400, rate = 6% p.a. and time = 2 years

Answer:

P=Rs. 6400,  R=6%,  T=2 yearsS.I. =P×R×T100=6400×6×2100    =Rs. 768Amount=P+S.I.=6400+768= Rs. 7168

Page No 165:

Question 2:

Find the simple interest and the amount when:

Principal = Rs 2650, rate = 8% p.a. and time = 212 years

Answer:

P=Rs. 2650, R=8%, T=212 years =52 years         

S.I.=  P×R×T100=2650×8×5100×2

                    =Rs. 530Amount=P+S.I.=2650+530=Rs. 3180

Page No 165:

Question 3:

Find the simple interest and the amount when:

Principal = Rs 1500, rate = 12% p.a. and time = 3 years 3 months.

Answer:

P=Rs.1500, R=12%, T=3+312=134 years              S.I.=P×R×T100=1500×12×13100×4    =Rs. 585Amount=P+S.I.              =1500+585              =Rs. 2085

Page No 165:

Question 4:

Find the simple interest and the amount when:

Principal = Rs 9600, rate = 712% p.a. and time = 5 months.

Answer:

P= Rs. 9600R=712% T=5 months =512 yearsS.I.=P×R×T100     =9600×15×5100×2×12    =Rs. 300Amount= P+ S.I.=9600+300=Rs. 9900

Page No 165:

Question 5:

Find the simple interest and the amount when:

Principal = Rs 5000, rate = 9% p.a. and time = 146 days.

Answer:

P=Rs.5000 , R=9% , T=146 days=146365 yearsS.I.=P×R×T100=5000×9×146100×365    =Rs. 180Amount=P+S.I.=5000+180=Rs. 5180

Page No 165:

Question 6:

Find the time when:

Principal = Rs 6400, SI = Rs 1152 and rate = 6% p.a.

Answer:

P=Rs. 6400, S.I. = Rs. 1152, R=6%      T =S.I.×100P×R=1152×1006400×6  =1152384   =3 years

Page No 165:

Question 7:

Find the time when:

Principal = Rs 9540, SI = Rs 1908 and rate = 8% p.a.

Answer:

P=Rs. 9540 ,  S.I.=Rs. 1908, R=8%T = S.I.×100P×R=1908×1009540×8   =104   =212 years

Page No 165:

Question 8:

Find the time when:

Principal = Rs 5000, amount = Rs 6450 and rate = 12% p.a.

Answer:

P=Rs. 5000,  A=Rs. 6450, R=12%      S.I.=AP                           =64505000                          =Rs. 1450T =S.I×100P×R=1450×1005000×12   =2912  =2512      =2 years 5 months



Page No 166:

Question 9:

Find the rate when:

Principal = Rs 8250, SI = Rs 1100 and time = 2 years.

Answer:

= Rs. 8250, S.I.=Rs. 1100, T=2 yearsR=S.I.×100P×T=1100×1008250×2   =1100165=6.67%

Page No 166:

Question 10:

Find the rate when:

Principal = Rs 5200, SI = Rs 975 and time = 212 years.

Answer:

   P= Rs. 5200 , S.I.=Rs. 975     [ T=212 years=52 years]               R=S.I.×100P×T=975×100×25200×5                 =19526=7.5%

Page No 166:

Question 11:

Find the rate when:

Principal = Rs 3560, amount = Rs 4521.20 and time = 3 years.

Answer:

P=Rs. 3560 , A=Rs. 4521.20 , T=3 yearsS.I.= AP =4521.203560    =Rs. 961.20    R =S.I.×100P×T=961.20×1003560×3   =96120×100100×3560×3   =9%

Page No 166:

Question 12:

Shanta borrowed Rs 6000 from the State Bank of India for 3 years 8 months at 12% per annum. What amount will clear off her debt?

Answer:

P=Rs 6000, R=12%, T=3 years 8 months = 3812=4412yearsS.I. =P×R×T100=6000×12×44100×12= Rs 2640A= P+S.I.                = 6000+2640               = Rs 8640

Page No 166:

Question 13:

Hari borrowed Rs 12600 from a moneylender at 15% per annum simple interest. After 3 years, he paid Rs 7070 and gave a goat to clear off the debt. What is the cost of the goat?

Answer:

P=Rs. 12600        R=15%             T=3 yearsS.I.=P×R×T100=12600×15×3100    =Rs. 5670A=Rs. 12600+Rs. 5670=Rs. 18270  Hari had to pay Rs. 18270 to the money lender, but he paid Rs. 7070 and a goat. Cost of the goat =Rs. 18270Rs. 7070                  =Rs. 11200

Page No 166:

Question 14:

The simple interest on a certain sum for 3 years at 10% per annum is Rs 829.50. Find the sum.

Answer:

Let the sum be Rs. P. S.I.=Rs. 829.50,  T=3 years, R=10%Now, P=S.I×100R×T  =829.50×10010×3  =82953= 2765Hence, the sum is Rs. 2765.

Page No 166:

Question 15:

A sum when reckoned at 712% per annum amounts to Rs 3920 in 3 years. Find the sum

Answer:

 Let the required sum be Rs. x.          A=Rs. 3920, R=712%, T=3 yearsNow, Now, S.I.=P×R×T100=x×15×32×100=9x40A=P+S.I.       = x+9x40=40x+9x40 =49x40  But the amount is Rs. 3920.  =>49x40=3920=>x=3920×4049=15680049=3200Hence, the required sum is Rs. 3200.

Page No 166:

Question 16:

A sum of money put at 11% per annum amounts to Rs 4491 in 2 years 3 months. What will it amount to in 3 years at the same rate?

Answer:

Given: R=11%, T=2 years 3 months = 2+312=2712 yearsLet the required sum be Rs. x.S.I.=P×R×T100=x×11×279100×124=99x400A=P+S.I.   =x+99x400=400x+99x400=499x400  But the amount is Rs. 4491.                    =>499x400=4491                    =>x=4491×400499=1796400499=3600Hence, the required sum is Rs. 3600.∴ S.I.=P×R×T100=3600×11×3100=Rs. 1188Amount=P+S.I.=3600+1188                          =Rs. 4788

Page No 166:

Question 17:

A sum of money invested at 8% per annum amounts to Rs 12122 in 2 years. What will it amount to in 2 years 8 months at 9% per annum?

Answer:

Let the required sum be Rs. x.S.I.=P×R×T100=x×8×2100=16x100 A=P+S.I.   =x+16x100=100x+16x100=116x100But the amount is Rs. 12122.                   =>116x100=12122                   =>x=12122×100116=10450Now, S.I.=P×R×T100=10450×93×328100×1241=Rs. 2508A=P+S.I.     = Rs. 10450 + Rs. 2508     = Rs. 12958

Page No 166:

Question 18:

At what rate per cent per annum will Rs 3600 amount to Rs 4734 in 312 years?

Answer:

P=Rs. 3600    A=Rs. 4734      T= 312=72 years   S.I.=AP                     =47343600                     =Rs. 1134                  R=S.I.×100P×T   =1134×100×23600×7=9%

Page No 166:

Question 19:

If Rs 640 amounts to Rs 768 in 2 years 6 months, what will Rs 850 amount to in 3 years at the same rate per cent per annum?

Answer:

P=Rs. 640, A=Rs. 768,  T=2 years 6 months =52 years  S.I.=AP                     =768640                     =Rs. 128                           R=S.I.×100P×T=128×100×2640×5=8% P=Rs. 850, R=8%, T=3 yearsS.I. =P×R×T100=850×8×3100=204010=Rs. 204A=P+S.I.                              =850+204     =Rs. 1054

Page No 166:

Question 20:

In what time will Rs 5600 amount to Rs 6720 at 8% per annum?

Answer:

P=Rs. 5600,  A=Rs. 6720, R=8% S.I.=AP                     =67205600                     =Rs. 1120T=S.I.×100P×R=1120×1005600×8=1120448=212 years

Page No 166:

Question 21:

A sum of money becomes 85 of itself in 5 years at a certain rate of simple interest. Find the rate of interest.

Answer:

Let the sum be Rs. x .               Amount=8x5S.I.=AP=8x5x                   =3x5Let the rate be R%.S.I.=P×R×T100=>3x5=x×R×5110020=>3x×20=R×x×5=>R=3×x×204x×5=12Hence, the rate of interest is 12%.

Page No 166:

Question 22:

A sum of money lent at simple interest amounts to Rs 783 in 2 years and to Rs 837 in 3 years. Find the sum and the rate per cent per annum.

Answer:

Amount in 3 years=(Principal+ S.I. for 3 years)=Rs. 837                   Amount in 2 years=(Principal+ S.I. for 2 years)=Rs. 783                    On subtracting:             S.I. for 1 year=(837783)=Rs. 54S.I. for 2 years=(541×2)=Rs108Sum=Amount for 2 yearsS.I. for 2 years=783108              =Rs. 675        P=Rs. 675, S.I.=Rs. 108 and  T=2 yearsR=S.I.×100P×T  =108×10050267527×21  =8%

Page No 166:

Question 23:

A sum of money lent at simple interest amount to Rs 4745 in 3 years and to Rs 5475 in 5 years. Find the sum and the rate per cent per annum.

Answer:

Amount in 5 years=(Principal+ S.I. for 5 years)=Rs. 5475                   Amount in 3 years=(Principal+ S.I. for 3 years)=Rs. 4745                    On subtracting:               S.I. for 2 years=(54754745)=Rs. 730S.I. for 3 years=(7302×3)=Rs1095Sum=Amount for 3 yearsS.I. for 3 years=47451095              =Rs. 3650 P=Rs. 3650, S.I.=Rs. 1095, T=3 yearsR=S.I.×100P×T  =1095×1003650×3  = 10%

Page No 166:

Question 24:

Divide Rs 3000 into two parts such that the simple interest on the first part for 4 years at 8% per annum is equal to the simple interest on the second part for 2 years at 9% per annum.

Answer:

Let the first part be Rs. x.  Second part =(3000x) S.I. on x at 8% per annum for 4 years=x×8×4211005025=8x25S.I. on (3000x) at 9% per annum =(3000x)×9×2110050                                                                  =270009x508x25=270009x50=>8x=(270009x)×251502=>16x=270009x=>16x+9x=27000=>x=270001080251=1080First part = Rs.1080 Second part =(30001080)=Rs. 1920

Page No 166:

Question 25:

Divide Rs 3600 into two parts such that if one part be lent at 9% per annum and the other at 10% per annum, the total annum income is Rs 333.

Answer:

Let the first part be Rs. x.           Second part =(3600x)S.I. on x at 9% per annum for 1 years=x×9×1100=9x100And, S.I. on (3600x) at 10% per annum =(3600x)×1×101100=3600x109x100+3600x10=333=>9x+3600010x100=333=>x+36000=33300=>x=3330036000=>x=2700=>x=2700First part = Rs. 2700 Second part =(36002700)=Rs900

Page No 166:

Question 1:

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The simple interest on Rs 6250 at 4% per annum for 6 months is

(a) Rs 125
(b) Rs 150
(c) Rs 175
(d) Rs 135

Answer:

(a) Rs.125Principal =Rs. 6250Simple Interest=4% per annumTime =6 months=12 yearsSimple Interest=P×R×T100Simple Interest=6250×4×1100×2Simple Interest=2502=Rs125

Page No 166:

Question 2:

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A sum amounts to Rs 3605 in 219 days at 5% per annum. The sum is

(a) Rs 3250
(b) Rs 3500
(c) Rs 3400
(d) Rs 3550

Answer:

(b)  Rs.3500

Amount =Rs. 3605Time =219365 days=219365 daysRate=5% per  annumAmount = Sum +Sum×Rate×Time100Amount = Sum (1+Rate×Time100)Sum=36051+5100×219365=3605×3650037595Sum= Rs. 3500

Page No 166:

Question 3:

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At simple interest a sum becomes 65 of itself in 212 years. The rate of interest per annum is

(a) 6%
(b) 712%
(c) 8%
(d) 9%

Answer:

(c) 8%

Let the sum be Rs.  x.Rate of interest = r%Time=212 years=52 yearsAmount=65× Sum Rate=?Amount =65×SumPrincipal + S.I. = AmountPrincipal+Principal×Rate×Time100=65×Principal=>x+xr×5100×2=65x=>x(1+5r100×2)=65x=>1+r40=65=>r=40×15=>r=8So, the rate of interest is 8%.



Page No 167:

Question 4:

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In what time will Rs 8000 amount to Rs 8360 at 6% per annum simple interest?

(a) 8 months
(b) 9 months
(c) 114 years
(d) 112years

Answer:

(b) 9 months

4.(b)Let the time be t years.Principal=Rs. 8000Amount=Rs. 8360Rate =6% per annumAmount=Principal(1+Rate×Time100)83608000=1+6×t100=>836080001=6t100=>t=(836080008000)×1006       =3608000×1006       =68×12 months        = 9 months

Page No 167:

Question 5:

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At what rate per cent annum simple interest will a sum double itself in 10 years?

(a) 8%
(b) 10%
(c) 12%
(d) 1212%

Answer:

(b) 10%

Let the sum be Rs. x and the rate be r%.A/Q:Amount =2x P+S.I.=2xP+P×R×T100=2x=>x(1+r×10100)=2x=>100+10r100=2=>10r=20010010r=100r=10010r=10

Page No 167:

Question 6:

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The simple interest at x% per annum for x years will be Rs x on a sum of

(a) Rs x
(b) Rs 100x
(c) Rs100x
(d) Rs100x2

Answer:

(c) Rs. 100x


Simple Interest=RsxRate= x% per annumTime = x yearsSimple Interest=Principal×Rate×Time100=>x=Principal×x×x100=>Principal=Rs100x

Page No 167:

Question 7:

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The simple interest on a sum for 5 years is 25 of the sum. The rate per cent per annum is

(a) 10%
(b) 8%
(c) 6%
(d) 1212%

Answer:

(b) 8%

Time=5 yearsSimple interest=25P=>P×Rate×Time100=25P=>Rate×5100=25Rate=2×1005×5=>Rate=8%

Page No 167:

Question 8:

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A borrows Rs 8000 at 12% per annum simple interest and B borrows Rs 9100 at 10% per annum simple interest. In how many years will their amounts be equal?

(a) 18 years
(b) 20 years
(c) 22 years
(d) 24 years

Answer:

(c) 22 years

R1=12%R2=10%P1=Rs.8000P2=Rs.9100Let their amounts be equal in T years.Amount1=S.I.1+P1                =P1×R1×T100+P1                =8000×12×T100+8000                = 960T+8000Amount2=S.I.2+P2                =P2×R2×T100+P2                =9100×10×T100+9100                = 910T+9100Amount1=Amount2 960T+8000=910T+9100960T-910T=9100-800050T=1100T=22 Hence, after 22 years their amounts will be equal.

Page No 167:

Question 9:

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A sum of Rs 600 amounts of Rs 720 in 4 years. What will it amount to if the rate of interest is increased by 2%?

(a) Rs 724
(b) Rs 648
(c) Rs 768
(d) Rs 792

Answer:

(c) Rs. 768

Let the rate be R %.S.I.= A-P     = 720-600     =Rs. 120Time=4 yearsR=100×SIP×T R=100×120600×4   =5Rate of interest=5%Now, R=(5+2)%=7%S.I.=P×R×T100  =600×7×4100  =Rs. 168Amount= SI+P              =600+168              = Rs. 768    

Page No 167:

Question 10:

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x, y and z are three sums of money such that y is the simple interest on x and z is the simple interest on y for the same time and same rate. Which of the following is correct?

(a) xyz = 1
(b) z2 = xy
(c) x2 = yz
(d) y2 = zx

Answer:

(d) y2 = zx

y=S.I. on x=x×R×T100             ...(i)z=S.I. on y=y×R×T100                ...(ii)Dividing equation (i) by (ii):yz=x×R×T100×100y×R×Tyz=xyy2=xz

Page No 167:

Question 11:

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In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?

(a) 114 years
(b) 134 years
(c) 214 years
(d) 234 years

Answer:

(a) 114 years

Rate=10% per annumSimple Interest=0.125 × Principal=>Principal×Rate×Time100=0.125×Principal=>Time10=0.125=>Time=1.25=114 years

Page No 167:

Question 12:

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At which sum will the simple interest at the rate of 334% per annum be Rs 210 in 213 years?

(a) Rs 1580
(b) Rs 2400
(c) Rs 2800
(d) none of these

Answer:

(b) Rs 2400
Rate=334% per annum      =154%  per annumTime=213 years       =73 yearsS.I. =154×73100=>P=210×100(154×73)=>P=600×4=>P= Rs 2400



Page No 168:

Question 1:

Find the simple interest on Rs 6300 at 8% per annum for 8 months.

Answer:

P=Rs 6300, R=8% , T=812 years        S.I.=P×R×T100=6300×8×82142100×12631=Rs 336

Page No 168:

Question 2:

What sum will amount to Rs 6600 in 2 years at 10% per annum simple interest?

Answer:

Let the sum be Rs x.S.I.=P×R×T100=x×10×211005=x5                      Now, A=P+S.IA=x+x5=6x5But the amount is Rs 6600.6x5=6600=>x=66001100×56=5500Hence, the required sum is Rs 5500.

Page No 168:

Question 3:

At what rate per cent per annum simple interest will Rs 3625 amount to Rs 4495 in 2 years?

Answer:

P=Rs 3625 , A=Rs 4495, T=2 yearsS.I.=AP                           =44953625                          =Rs 870S.I.=P×R×T100=>870=3625×R×2100=>R=870×1003625×2=>R=870007250=12%

Page No 168:

Question 4:

In what time will Rs 3600 amount to Rs 4410 at 9% per annum simple interest?

Answer:

P=Rs. 3600, A=Rs. 4410, R=9%           S.I.=A      =44103600                    =Rs. 810T=S.I.×100P×R=810×1003600×9=9036=212 years

Page No 168:

Question 5:

At what rate per cent per annum simple interest will a sum double itself in 12 years?

Answer:

 Let the sum be Rs x.   Amount =Rs 2x   S.I.=(2xx)=Rs xTime=12 years  P=x,  S.I.=x, T=12 years R=100×S.I.P×T=100×xx×12=8.3%

Page No 168:

Question 6:

A sum of money becomes 43 of itself in 6 years at a certain rate of simple interest. Find the rate of interest.

Answer:

Let the sum be Rs x.        Amount =43xS.I.=AP=43xx                =x3Let the rate be R%.S.I.=P×R×T100=>x3=x×R×6100=>R=x×100x×6×3=10018=5.55Hence, the rate of interest is 5.55%.

Page No 168:

Question 7:

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At simple interest a sum becomes 4940 of itself in 212 years. The rate of interest per annum is
(a) 7%
(b) 8%
(c) 9%
(d) 12%

Answer:

(c) 9%
Let the sum be Rs x.           A=49x40We know:A=P+S.I.S.I. =AP       =(49x40x)       =49x40x40       =9x40 Let the rate be R% per annum.                    S.I.=P×R×T100=>9x40=x×R×5110020×2=>R=9×201×214021=>R=9

Page No 168:

Question 8:

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A sum amounts to Rs 3626 in 219 days at 6% per annum simple interest. The sum is

(a) Rs 3000
(b) Rs 3200
(c) Rs 3500
(d) Rs 3600

Answer:

(c) 3500
A=Rs 3626, R=6%, T=219 days=219365yearsLet the required sum be Rs  x.S.I.=P×R×T100=x×6×219100×365=1314x36500A=P+S.I.     =x+1314x36500    =36500x+1314x36500    =37814x36500But the amount is Rs 3626.37814x36500=3626x=3626259×36500378142701=3500The required sum is Rs 3500.

Page No 168:

Question 9:

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In what time will Rs 6000 amount to Rs 6360 at 8% per annum simple interest?

(a) 9 months
(b) 8 months
(c) 114  years
(d) 112 years

Answer:

(a) 9 months

P=Rs 6000, A=Rs 6360, R=8%      S.I.=AP                 =63606000                 =Rs. 360T=S.I.×100P×T=360×1006000×8                   =68 years                   =68×12 months                  =728           =9 months

Page No 168:

Question 10:

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The simple interest on a sum for 5 yars is 35 of the sum. The rate per cent per annum is
(a) 8%
(b) 10%
(c) 12%
(d) 1212%

Answer:

(c) 12% Let the sum be Rs x.S.I.=Rs 35   Let the rate be R% per annum.S.I.=P×R×T100=x×R×5100=Rx203x5=Rx20=>R=3x×205x=12%

Page No 168:

Question 11:

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The simple interest at x% per annum for x years will be Rs x on a sum of

(a) Rs x
(b) Rs 10 x
(c) Rs 100 x
(d) Rs 100x

Answer:

(d) Rs 100xLet the sum be Rs P.Time=x yearsRate of interest, r=x% per annumS.I.=Rs xSimple Interest =P×R×T100   =>x =P×x×x100   =>P=x×100x×xP=(100x)

Page No 168:

Question 12:

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At what rate per cent per annum simple interest will a sum double itself in 10 years?

(a) 8%
(b) 10%
(c) 12%
(d) 1212%

Answer:

(b) 10%Let the sum be Rs x.Amount=Rs 2xTime=10 yearsS.I.=AP=2xx                   =Rs xS.I.=P×R×T100=>x=x×R×10100=>R=x×100x×10=>R=10

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Question 13:

Fill in the blanks.

(i) P=100×(......)R×T
(ii) R=100×SI(......)×T
(iii) At (......)% per annum simple interest a sum doubles itself in 10 years.
(iv) At simple interest a sum becomes 65 of itself in 212 years. The rate of interest is (......)% per annum.

Answer:

(i)P=100×S.I.R×T(ii)R=100×S.I.(P)×T(iii)10% Let the sum be Rs x. Amount= Rs 2xS.I.=A-P=2x-x=Rs xLet the rate of inetrset be R%.Time=10 yrsS.I.=P×R×T100x=x×R×10100R=10010 R =10(iv) 8% Let the sum be Rs x. Amount= Rs 65xS.I.=A-P=65x-x=Rs x5Let the rate of inetrset be R%.Time=2.5 yrsS.I.=P×R×T100x5=x×R×2.5100R=1002.5×5 R =8

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Question 14:

Write 'T' for true and 'F' for false

(i) Simple interest on Rs x for x years is Rs x. Then, the rate of interest is x% per annum.
(ii) Rate = 100×SIP×T.
(iii) A sum doubles itself at simple interest at 10% per annum in 10 years.
(iv) Simple interest on Rs 1000 at 5% per annum for 73 days is Rs 10.

Answer:

(i) FalseS.I.=P×R×T100x=x×R×x100R=100×xx×xR=100x%(ii) True(iii) TrueLet the sum be Rs x.S.I.=P×R×T100S.I.=x×10×10100S.I.=Rs xAmount= S.I.+P=x+x=Rs 2x(iv) TrueP=Rs 1000 , R=5%, T=73 days=73365 yrsS.I.=P×R×T100   =1000×5×73100×365   =Rs 10



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