RS Aggarwal 2017 Solutions for Class 8 Math Chapter 9 Percentage are provided here with simple step-by-step explanations. These solutions for Percentage are extremely popular among class 8 students for Math Percentage Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RS Aggarwal 2017 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 RS Aggarwal 2017 Solutions. All RS Aggarwal 2017 Solutions for class 8 Math are prepared by experts and are 100% accurate.

Page No 121:

Question 1:

Express each of the following as a fraction:
(i) 48%
(ii) 220%
(iii) 2.5%

Answer:

i 48%=48100=1225

ii 220%=220100=115

iii 2.5%=2.5100=251000=140

Page No 121:

Question 2:

Express each of the following as a decimal:
(i) 6%
(ii) 72%
(iii) 125%

Answer:

i 6%=6100=0.06

ii 72%=72100=0.72

iii 125%=125100=1.25

Page No 121:

Question 3:

Express each of the following as a percentage:
(i) 925
(ii) 3125
(iii) 125

Answer:

i 925=(925×100)%=(9×4)%=36%


ii 3125=(3125×100)%=2.4%

iii 125=(125×100)%=240%

Page No 121:

Question 4:

Convert the ratio 4 : 5 to percentage.

Answer:

4 :5 =45=  45×100%= 80%

Page No 121:

Question 5:

Express 125% as a ratio.

Answer:

125%=125100=54 = 5:4

Page No 121:

Question 6:

Which is largest in 623%,320 and 0.14?

Answer:

​       We have: 623%=203%             =203×1100             =115             =0.06  
      Also, 320=0.15
      The third number is 0.14.Clearly, 0.15 is the largest.Hence, 320 is the largest.



Page No 122:

Question 7:

(i) What per cent of 150 is 96?
(ii) What per cent of 5 kg is 200 g?
(iii) What per cent of 2 litres is 250 mL?

Answer:

i Required percentage=96150×100%=64%
                                    
(ii) Required percentage=2005×1000×100%= 4%
                                  
iii Required percentage=2502×1000×100%= 12.5%
                                    

Page No 122:

Question 8:

Find 412% of Rs 3600.

Answer:

412%=92×100 9200  of Rs 3600=9200×3600=Rs 162

Page No 122:

Question 9:

If 16% of a number is 72, find the number.

Answer:

Let the number be x.16% of x is 72.16100×x=7216x=72×10016x=7200x=720016=450 The required number is 450.

Page No 122:

Question 10:

A man saves 18% of his monthly income. If he saves Rs 1890 per month, what is his monthly income?

Answer:

Let Rs x be his monthly income.His savings =18% of Rs x

                =Rs x×18100=Rs 9x50
Now, 9x50=1890x=Rs 1890×509x=Rs 10500 His monthly income is Rs.10500.

Page No 122:

Question 11:

A football team wins 7 games, which is 35% of the total games played. How many games were played in all?

Answer:

Let x be the total number of games played. Percentage of games won=35% of x
                             =x×35100=35x100
Now, 35x100=7      x=7×10035      x=20 The total number games played is 20.

Page No 122:

Question 12:

Amit was given an increment of 20% on his salary. If his new salary is Rs 15300, what was his salary before the increment?

Answer:

Let Rs x be Amit's old salary.His salary after increment will be Rs x+20100xAccording to the question, we have:x+20100x=15300100x+20x100=15300       LCM=100120x100=15300120x=15300×100x=15300×100120x=12750 The old salary is Rs 12,750.

Page No 122:

Question 13:

Sonal attended her school on 204 days in a full year. If her attendance is 85%, find the number of days on which the school was opened.

Answer:

Let x be the number of days the school was opened.Number of days Sonal attended school=204 daysPercentage of her attendance=85% of x
                                =x×85100=85x100
Now, 85x100=204      x=204×10085      x=240 The school was opened for 240 day.

Page No 122:

Question 14:

A's income is 20% less than that of B. By what per cent is B's income more than A's?

Answer:

Let B's income be Rs 100Then, A's income=Rs 80Therefore, B's income is more thanA's income by = 100-8080×100% = 2080×100% = 25%                                   
                                                          =Rs125
 B's income is more than that of A's by 125-100%, i.e., 25%.

Page No 122:

Question 15:

The price of petrol goes up by 10%. By how much per cent must a motorist reduce the consumption of petrol so that the expenditure on it remains unchanged?

Answer:

Let the consumption of petrol originally be 1 unit and let its cost be Rs 100.New cost of 1 unit of petrol=Rs 110Now, Rs 110 will yield 1 unit of petrol.i.e., Rs 100 will yield 1110×100, i.e., 1011 units of petrol.
                    
Now, reduction in consumption=1-1011=111unit
Percentage of reduction=111×11×100%=9111%
 A motorist must reduce the consumption of petrol by 9111%.

Page No 122:

Question 16:

The population of a town increases by 8% annually. If the present population is 54000, what was it a year ago?

Answer:

Let x be the population of the town a year ago.Then, present population=108% of x
                             =x×108100=27x25
Now, 27x25=54000      x=54000×2527      x=50000
Hence, the population of the town a year ago was 50000.

Page No 122:

Question 17:

The value of a machine depreciates every year by 20%. If the present value of the machine be Rs 160000, what was its value last year?

Answer:

Let Rs x be the value of the machine last year.Then, present value=80% of Rs x
                       =Rsx×80100=Rs4x5
Now, 4x5=160000      x=160000×54      x=40000×5=200000
Hence, the value of the machine last year was Rs 2,00,000.

Page No 122:

Question 18:

An alloy contains 40% copper, 32% nickel and rest zinc. Find the mass of zinc in one kg of the alloy.

Answer:

Mass of the alloy=1 kgPercentage of copper=40%Percentage of nickel=32%Percentage of zinc=100-40+32%
                     =28%                     
 Mass of zinc in 1 kg of alloy=28100×1 kg
                                     =0.28 kg=0. 28×1000 g=280 g

Page No 122:

Question 19:

Balanced diet should contain 12% of proteins, 25% of fats and 63% of carbohydrates. If a child needs 2600 calories in his food daily, find in calories the amount of each of these in his daily food intake.

Answer:

Amount of protein=12% of 2600
                       =2600×12100=312 cal
Amount of fat=25% of 2600
                 =2600×25100=650 cal
Amount of carbohydrate=63% of 2600
                             =2600×63100=1638 cal

Page No 122:

Question 20:

Gunpowder contains 75% nitre and 10% sulphur. Find the amount of gunpowder which carries 9 kg nitre. What amount of gunpowder would contain 2.5 kg sulphur?

Answer:

Let x be the amount of gunpowder.Amount of nitre=75%Let x kg be the amount of gunpowder containing 9 kg of nitre. i.e., 75% of x=9 kg
  x×75100=975x100=9x=9×10075x=12 kg
Hence, 12 kg of gunpowder contains 9 kg of nitre.Now, amount of sulphur=10%Let x kg be the amount of gunpowder containing 2.5 kg of sulphur.i.e., 10% of x=2.5 kg
  x×10100=2.510x100=2.5x10=2.5x=2.5×10x=25 kg
Hence, 25 kg of gunpowder contains 2.5 kg of sulphur.

Page No 122:

Question 21:

Divide Rs 7000 among A, B and C such that A gets 50% of what B gets and B gets 50% of what C gets.

Answer:

Let  Rs x be the amount of money recieved by C.Then, amount of money B gets =50% of Rs xAmount of money A gets=50% of B                                         =25% of Rs xNow, x+50% of Rs x+25% of Rs x=Rs 7000x+x×50100+x×25100=Rs 7000x+50x100+25x100=Rs 7000x+50x100+25x100=Rs 7000175x100=Rs 7000x=Rs 7000×100175x=Rs 4000
 C gets Rs 4000.Amount of money B gets=50% of Rs x
                                    =50% of Rs 4000=Rs 4000×50100=Rs 2000

Amount of money A gets=25% of Rs x
                                   =25% of Rs 4000=Rs 4000×25100=Rs 1000

Page No 122:

Question 22:

Find the percentage of pure gold in 22-carat gold, if 24-carat gold is 100% pure.

Answer:

22 carat gold contains 22 parts pure gold out of 24 parts.Also, 24 carat gold is given to be 100% pure. Percentage of pure gold in 22 carat gold=2224×100% 
                                                   =9123%
Hence, 22 carat gold contains 9123% of pure gold.

Page No 122:

Question 23:

The salary of an officer is increased by 25%. By what per cent should the new salary be decreased to restore the original salary?

Answer:

Let the original salary be Rs 100
Then, after increment of 25% the salary becomes
= 1001+25100 = 100125100 = Rs 125

To restore the original salary, let the new salary be decreased by x%.
Thus, we get

1251-x100 = 1001-x100 = 100125 = 45x100 = 15x = 1005 =20 %
Therefore, the new salary must be reduced by 20% to restore the original salary.



Page No 123:

Question 1:

Tick (✓) the correct answer:
35=?
(a) 30%
(b) 40%
(c) 45%
(d) 60%

Answer:

(d) 60%

35=35×100%     =60%

Page No 123:

Question 2:

Tick (✓) the correct answer:
0.8% when expressed as a decimal, is
(a) 0.08
(b) 0.008
(c) 8
(d) 0.8

Answer:

(b) 0.008
0.8%=0.8100          =0.008

Page No 123:

Question 3:

Tick (✓) the correct answer:
6 : 5 when expressed as a percentage, is
(a) 8313%
(b) 90%
(c) 120%
(d) 6.5%

Answer:

(c) 120%
6:5=65      =65×100%      =120%

Page No 123:

Question 4:

Tick (✓) the correct answer:
5% of a number is 9. The number is
(a) 45
(b) 90
(c) 135
(d) 180

Answer:

(d) 180

Let x be the required number. Then, we have:5% of x=9x×5100=95x100=9x=9×1005x=180

Page No 123:

Question 5:

Tick (✓) the correct answer:
What per cent of 92 is 120?
(a) 75%
(b) 3313%
(c) 13313%
(d) none of these

Answer:

(c) 13313%
Required percentage =12090×100%                                    =13313%

Page No 123:

Question 6:

Tick (✓) the correct answer:
What per cent of 10 kg is 250 g?
(a) 25%
(b) 5%
(c) 10%
(d) 2.5%

Answer:

(d) 2.5%

Required percentage=25010×1000×100%=2.5%

Page No 123:

Question 7:

Tick (✓) the correct answer:
40% of ? = 240
(a) 60
(b) 600
(c) 6000
(d) 960

Answer:

(b) 600

Let the required number be x. Then, we have:40% of x=240x×40100=24040x100=240x=240×10040x=600

Page No 123:

Question 8:

Tick (✓) the correct answer:
?% of 400 = 60
(a) 6
(b) 12
(c) 15
(d) 20

Answer:

(c) 15

Let the required number be x. Then, we have:x% of 400=60400×x100=60400x100=604x=60x=604x=15

Page No 123:

Question 9:

Tick (✓) the correct answer:
(180% of ?) ÷ 2 = 504
(a) 400
(b) 480
(c) 600
(d) 560

Answer:

(d) 560

Let the required number be x. Then, we have:180% of x÷2=504x×180100÷2=504180x100÷2=504180x100×12=5049x10=504x=504×109x=560

Page No 123:

Question 10:

Tick (✓) the correct answer:
20% of Rs 800 = ?
(a) Rs 160
(b) Rs 16
(c) Rs 1600
(d) none of these

Answer:

(a) Rs 160
20% of Rs 800=Rs 800×20100
                     =Rs 160

Page No 123:

Question 11:

Tick (✓) the correct answer:
In an examination, Nitin gets 98 marks. This amounts to 56% of the maximum marks. What are the maximum marks?
(a) 75
(b) 150
(c) 175
(d) 225

Answer:

(c) 175

Let the maximum marks be x. Then, we have:56% of x=x×56100
            =56x100
Now, 56x100=98x=98×10056x=175

Page No 123:

Question 12:

Tick (✓) the correct answer:
A number is first increased by 10% and then reduced by 10%. The number
(a) does not change
(b) decrease by 1 %
(c) increases by 1 %
(d) none of these

Answer:

(b) decrease by 1 %

Let x be the number.A 10% increase will give a new number, 110100x = 1110xThe number is then reduced by 10%.The new number will be 901001110x=9901000x=99100xDifference = x - 99100x=1100xPercentage of decrease = 1100x × 1x×100  = 1%


     

Page No 123:

Question 13:

Tick (✓) the correct answer:
A period of 4 hours 30 min is what per cent of a day?
(a) 1834%
(b) 20%
(c) 1623%
(d) 19%

Answer:

(a) 1834%

4 h 30 min=4×60×60+30×60
               =16200 sec
24 h=24×60×60
      =86400 sec
Now, 1620086400×100%=1834%

Page No 123:

Question 14:

Tick (✓) the correct answer:
In an examination, 65% of the total examinees passed. If the number of failures is 420, the total number of examinees is
(a) 500
(b) 1000
(c) 1200
(d) 1625

Answer:

(c) 1200

Let x be the total number of examinees.Percentage of the examinees passed=65%Percentage of the examinees failed=35%Number of the examinees failed=35% of x
                                 =x×35100=35x100
Now, 35x100=420x=420×10035x=1200



Page No 124:

Question 15:

Tick (✓) the correct answer:
A number exceeds 20% of itself by 40. The number is
(a) 50
(b) 60
(c) 80
(d) 320

Answer:

(a) 50

Let x be the required number. Then, we have: 20% of x+40=xx×20100+40=x20x100+40=x20x100-x=-40-80x100=-40x=40×10080x=50

Page No 124:

Question 16:

Tick (✓) the correct answer:
A number decreased by 2712% gives 87. The number is
(a) 58
(b) 110
(c) 120
(d) 135

Answer:

(c) 120

Let the required number be x. Then, we have:    x-2712% of x=87x-552% of x=87x-x×552×1100=87x-11x40=8729x40=87x=87×4029x=120

Page No 124:

Question 17:

Tick (✓) the correct answer:
0.05 is what per cent of 20?
(a) 25%
(b) 2.5%
(c) 0.25%
(d) 0.025%

Answer:

(c) 0.25%
Required percentage=0.0520×100%=0.25%

Page No 124:

Question 18:

Tick (✓) the correct answer:
One-third of 1206 is what per cent of 134?
(a) 3%
(b) 30%
(c) 20%
(d) 300%

Answer:

(d) 300%

Required percentage=12063×1134×100%=300%

Page No 124:

Question 19:

Tick (✓) the correct answer:
x% of y is y% of?
(a) x
(b) 100x
(c) x100
(d) y100

Answer:

(a) x

Let the required number be z. Then, we have:x% of y=y% of zy×x100=z×y100yx100=zy100z=yx100×100yz= x

Page No 124:

Question 20:

Tick (✓) the correct answer:
What per cent of 27 is 135?
(a) 2.5%
(b) 10%
(c) 20%
(d) 25%

Answer:

(a) x
Required percentage=135×72×100%=10%



Page No 125:

Question 1:

Express:
(i) 24% as a fraction;
(ii) 105% as a decimal;
(iii) 4 : 5 as a percentage;
(iv) 56% as a ratio.

Answer:

i 24%=24100              =625

ii 105%=105100                 =1.05iii 4 : 5=45               =45×100%                =80%iv 56%=56100                =1425                =14 : 25

Page No 125:

Question 2:

If 34% of a number is 85, find the number.

Answer:

Let the required number be x. Then, we have:34% of x=85x×34100=8534x100=85x=85×10034x=250 Hence, the required number is 250.

Page No 125:

Question 3:

The value of a machine depreciates every year by 10%. If the present value of the machine is Rs 54000, what was its value last year?

Answer:

Let the value of the machine last year be Rs x.Then, its present value=90% of Rs x
                                 =Rs x×90100=Rs 90x100
Now, 90x100=54000      x=54000×10090      x=Rs 60000
Hence, the value of the machine last year was Rs 60,000.

Page No 125:

Question 4:

An alloy contains 30% copper, 42% nickel and rest zinc. Find the mass of zinc in 1 kg of alloy.

Answer:

Percentage of copper=30%Percentage of nickel=42%Percentage of zinc=100-30+42%
                      =28%
                    
 Mass of zinc in 1 kg of the alloy=28100×1 kg=0.28 kg=280 g
                                          

Page No 125:

Question 5:

In a class, 60% of the total number of students are boys and there are 14 girls. How many students are there in the class?

Answer:

Let the total number of students be x. Then, we have:Percentage of boys=60%Percentage of girls=40% Number of girls=40% of  x
                      =x×40100=40x100
Now, 40x100=14x=14×10040x=35

 Total number of students=35

Page No 125:

Question 6:

Which is largest in 813%,425 and 0.15?

Answer:

We have:813%=253%           =253×1100           =112           =0.083
Also, 425=0.16The third number is 0.15.Clearly, 0.16 is the largest.i.e., 425 is the largest.

Page No 125:

Question 7:

Mark (✓) against the correct answer:
What per cent of 29 is 145?
(a) 2.5%
(b) 5%
(c) 7.5%
(d) 10%

Answer:

(d) 10%

Required percentage=145×92×100%=10%

Page No 125:

Question 8:

Mark (✓) against the correct answer:
A number decreased by 30% gives 84. The number is
(a) 90
(b) 110
(c) 120
(d) 135

Answer:

(c) 120

Let the required number be x
x-30% of x=84x-x×30100=84x-30x100=8470x100=84x=84×10070x=120

Page No 125:

Question 9:

Mark (✓) against the correct answer:
(?)% of 320 is 48?
(a) 25%
(b) 15%
(c) 14%
(d) 9%

Answer:

(b) 15%

Let the required number be x. Then, we have:x% of 320=48320×x100=48320x100=48x=48×100320x=15%

Page No 125:

Question 10:

Mark (✓) against the correct answer:
What per cent of 45 is 54?
(a) 8313%
(b) 104%
(c) 108%
(d) 120%

Answer:

(d) 120%
Required percentage=5445×100%=120%

Page No 125:

Question 11:

Mark (✓) against the correct answer:
A number exceeds 25% of itself by 60. The number is
(a) 75
(b) 45
(c) 80
(d) 65

Answer:

(c) 80

Let the required number be x. Then, we have:25% of x+60=xx×25100+60=x25x100+60=x25x100-x=-60-75x100=-60x=60×10075x=80

Page No 125:

Question 12:

Mark (✓) against the correct answer:
5% of which number is 12?
(a) 120
(b) 180
(c) 240
(d) 320

Answer:

(c) 240

Let the required number be x. Then, we have:     5% of x=12x×5100=125x100=12x=12×1005x=240

Page No 125:

Question 13:

Fill in the blanks.
(i) 712% of Rs 1200 = .........
(ii) 240 mL is ......... % of 3 L.
(iii) If x% of 35 is 42, then x = .........
(iv) 125 = .........%.
(v) 120 = (.........)% of 80.

Answer:

i 712% of Rs 1200=152% of Rs 1200
                        =Rs 152×1100×1200=Rs 90
Hence, 712% of Rs 1200=Rs 90

ii Required percentage=2403×1000×100%=8%Hence, 240 ml is 8% of 3 L.

iii x% of 35=42        35×x100=42        35x100=42        x=42×10035        x=120% If x% of 35 is 42, then x=120%. 

iv 125×100%=240%Hence, 125=240%

v Let the required number be x. Then, we have:120=x% of 8080×x100=120  80x100=120  x=120×10080  x=150% 120=150% of 80



Page No 126:

Question 14:

Write 'T' for true and 'F' for false for each of the following:
(i) 6% of 8 is 48.
(ii) 6 : 5 = 30%.
(iii) 35=60%.
(iv) 6 hours = 25% of a day.

Answer:

i 6% of 8=8×6100                   =0.48Hence, it is false.

ii 6:5=65            =65×100%            =120%Hence, it is false.

iii 35=35×100%             =60%Hence, it is true.

iv 6 hours  =624×100%=25%
Hence, it is true.



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