8. Comparing Quantities – Class 8 Mathematics NCERT Chapter 8 Complete Guide (CBSE)
NCERT Class 8 Mathematics Chapter 8: Comparing Quantities – All Exercise Solutions | CBSE Board
Chapter 8: Comparing Quantities
Exercise 8.1
1. Find the ratio of the following: (a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour. (b) 5 m to 10 km (c) 50 paise to Rs 5 .
Solution: (a) We have,
The ratio = 
(b) We have,
The ratio = 
[Note : 1km = 1000 m ]
(c) We have,
The ratio = 
[Note : Rs 1 = 100 Paise ]
2. Convert the following ratios to percentages: (a) 3 : 4 (b) 2 : 3
Solution: (a) We have, 
(b) We have, 
3. 72% of 25 students are interested in mathematics. How many are not interested in mathematics?
Solution: The students are interested in mathematics 
The students are not interested in mathematics 
Therefore, the percentage of the students 
4. A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all ?
Solution: Total number of matches = 100 .
Therefore, the number of matches 
5. If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning ?
Solution: Suppose , the money of Chameli is Rs 100 .
The money spent by Chameli 
The money left after spent by chameli = Rs 100 – Rs 75 = Rs 25
Therefore, the money of Chemali in beginning 
6. If 60% people in a city like cricket, 30% like football and the remaining like other games, then what per cent of the people like other games ? If the total number of people is 50 lakh, find the exact number who like each type of game.
Solution: Total number of people = 50,00,000 .
The percentage of other game = (100 – 60 – 30)% = (100 – 90) % = 10 %
The number people who like cricket 
The number people who like football 
The number people who like other game 
Exercise 8.2
1. A man got a 10% increase in his salary. If his new salary is Rs 1,54,000, find his original salary.
Solution: Let 
be the original salary .
Given, new salary (A) = Rs 154000 and increase in salary (R) = 10 %
We know that, 
Therefore, the original salary is Rs 1,40,000 .
2. On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the per cent decrease in the people visiting the Zoo on Monday?
Solution: Given , the number of visitor on Sunday = 845 and on Monday = 169 .
The decrease the number of visitor = 845 – 169 = 676
The per cent decrease in the people visiting the Zoo on Monday
3. A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16%. Find the selling price of one article.
Solution: Price of each articles 
Now , Profit 
Thus , the selling price of one article = Rs (30+4.8) = Rs 34.8
4. The cost of an article was Rs 15,500. Rs 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.
Solution: The total cost of an article = The cost of an article + The cost of repairs
= Rs (15500 +450) = Rs 15950
Profit 
Thus , the selling price of the article = Rs (15950 + 2392.50) = Rs 18342.50
5. A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole transaction.
Solution: Given, Price of a VCR = Rs 8000 and loss 4 % (This means cost price is Rs 100 , then selling price is Rs (100 – 4) =Rs 96).
Selling price of a VCR 
Again , price of a TV = Rs 8000 and profit 8% (This means cost price is Rs 100 , then selling price is Rs (100 + 8) =Rs 108).
Selling price of a VCR 
Total cost price = Rs 8000 +Rs 8000 = Rs 16000
And total selling price = Rs 7680 + Rs 8640 = Rs 16320
Since , total SP > total CP
Profit = Rs (16320 - 16000) = Rs 320
Therefore , the gain percent on the whole transaction 
6. During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at Rs 1450 and two shirts marked at Rs 850 each?
Solution: Marked price = Cost of a jeans + Cost of two shirts
= Rs 1450 +Rs 2×850
=Rs (1450 + 1700) = Rs 3150
and the discount percentage = 10 %
Discount 
The sale price = Marked price – discount = Rs (3150 – 315) = Rs 2835
Therefore , the customer has to pay Rs 2835 .
7. A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss. (Hint: Find CP of each)
Solution: The cost price of each buffaloes = Rs 20,000 and gain 5% .
This means if CP is Rs 100 then SP is Rs (100 + 5 )= Rs 105 .
Selling price 
Again , the cost price of each buffaloes = Rs 20,000 and loss 10 % .
This means if CP is Rs 100 then SP is Rs (100 – 10 )= Rs 90 .
The cost price 
Total selling price = Rs (20000 + 20000) = Rs 40000
And total cost price = Rs (19047.62 + 22222.22) = Rs 41269.84
Since total cost price > selling price .
Loss = Rs (41269.84 – 40000) = Rs 1269.84
8. The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.
Solution: The price of a TV = Rs 13000 and rate 12% .
On Rs 13000 , the tax paid would be 
Therefore, the amount that Vinod will have to pay = The Price of a TV + Sales tax = Rs (13000 + 1560) = Rs14560
9. Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs 1,600, find the marked price.
Solution: let the marked price of the skates is Rs 100 .
Then selling price = Rs (100 – 20) = Rs 80
The marked price 
10. I purchased a hair-dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added.
Solution: Let the original price of the article be Rs 100 and VAT = 8 %
Price after VAT in including = Rs 108 .
When the selling price is Rs 118 then original price = Rs 100 .
When the selling price is Rs 5400 then original price 
Therefore, the price before VAT was Rs 5000 .
11. An article was purchased for Rs 1239 including GST of 18%. Find the price of the article before GST was added ?
Solution: Let the original price of the article be Rs 100 and GST = 18 %
Price after GST in included = Rs (100+18) = Rs 118
When the selling price is Rs 118 then original price = Rs 100 .
When the selling price is Rs 1239 then original price 
Exercise 8.3
1. Calculate the amount and compound interest on
(a) Rs10,800 for 3 years at 
per annum compounded annually.
(b) Rs 18,000 for 
years at 10% per annum compounded annually.
(c) Rs 62,500 for 
years at 8% per annum compounded half yearly.
(d) Rs 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify).
(e) Rs 10,000 for 1 year at 8% per annum compounded half yearly.
Solution: (a) Here , 
, 
, 
, 
We have , 
Amount = Rs 15377.34
Compound interest = A – P = 15377.34 – 10800 = Rs 4577.34
(b) Here, , 
, 
, 
We have ,
Simple interest for 2 years = Rs (21780 – 18000) = Rs 3780
For next half year ,
Simple Interest 
Compound interest = Rs (3780 + 1089) = Rs 4869
Amount = P + C.I = Rs (18000 + 4869) = Rs 22869
(c) Here , , 
, Year 
We know that , 
C.I = A – P = Rs (70304 – 62500) = Rs 7804
(d) Here , , 
, Year 
We know that , 
The compound interest = A – P = Rs (8736.20 – 8000) = Rs 736.20 .
(e) Here, , 
, 
, 
We know that , 
The compound interest = Rs (10816 – 10000) = Rs 816 .
2. Kamala borrowed Rs 26,400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? (Hint: Find A for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for 
years).
Solution: Here , P = Rs 26,400 , R = 15 % ,and 2 years 4 months 
Firstly , for 2 years in CI ,
We have , 
S.I for 2 years = Rs (34914 – 26400) = Rs 8514
Next , for 1/3 year in SI .
Simple interest 
C.I. = Rs (8514 + 1745.70) = Rs 10259.70
Amount = P + CI = Rs (26400 + 10259.70) = Rs 36659.70
3. Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
Solution: Here , P = Rs 12500 , R = 12 % ,n = 3
For Simple Interest ,
S.I 
For CI : Here, P = Rs 12500 , R = 10 % ,n = 3
Amount 
Compound interest = A – P = Rs (16637.50 – 12500) = Rs 4137.50
Fabina pay more interest than Radha .
Fabina pay = Rs (4500 – 4137.50 ) = Rs 362.5
4. I borrowed Rs 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?
Solution: Here , P = Rs 12000 , R = 6 % ,n = 2
For Simple Interest ,
Simple interest 
For CI : Here, P = Rs 12000 , R = 6 % ,n = 2
Amount 
Compound interest = A – P = Rs (13483.20 – 12000) = Rs 1483.20
Pay extra amount = Rs (1483.20 – 1440 ) = Rs 43.20
5. Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get
(i) after 6 months ? (ii) after 1 year ?
Solution: (i) Here , P = Rs 60000 , R = 12% , n = 6 month 
Simple interest 
Amount = P + S.I = Rs (60000 + 3600) = Rs 63600
(ii) Here, P = Rs 60000 , 
and n = 1year
We have, 
Therefore, the amount is Rs 67416 .
6. Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 112
years if the interest is
(i) compounded annually. (ii) compounded half yearly.
Solution: (i) Here , P = Rs 80,000 , R = 10% and 
and half years
For 1 year :
We have, 
Interest of 1 year = Rs (88000 – 80000) = Rs 8000
For half year :
Simple interest 
Total Compound interest = Rs (8000 + 4400) = Rs 12400
Amount = P + C.I. = Rs (80000+12400) = Rs 92400
(ii) Here , P = Rs 80000 , 
and 
year
We have , 
7. Maria invested Rs 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find : (i) The amount credited against her name at the end of the second year. (ii) The interest for the 3rd year.
Solution: Here , P = Rs 8000 , R = 5 % and n = 2 years
We have, 
(ii) Here, P = Rs 8000 , R = 5 % and n = 3 years
We have, 
Compound interest = A – P = Rs (9261 – 8820) = Rs 441
8. Find the amount and the compound interest on Rs 10,000 for years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
Solution: Here , P = Rs 10000 , R = 10% and 
We have , 
Compound interest = Rs (11576.25 – 10000) = Rs 1576.25
For 1 year (i.e., annually) , then n = 1 year , R = 10 %
Simple interest 
Here , P = Rs 10000 + Rs 1000 = Rs 11000
Simple interest for 
Total interest = Rs (1000+550) = Rs 1550
The difference interest = Rs 1576.25 – Rs 1550 = Rs 26.25
Yes , this interest is more than the interest he would get if it were compounded annually .
9. Find the amount which Ram will get on Rs 4096, if he gave it for 18 months at 
per annum, interest being compounded half yearly.
Solution: Here , P = Rs 4096 , 
and 
We know that , 
10. The population of a place increased to 54,000 in 2003 at a rate of 5% per annum
(i) find the population in 2001. (ii) what would be its population in 2005?
Solution: Let 
be the population in 2001 .
Given , the population in 2003 is 54,000
Here , A = 54000 , R = 5 % and n = 2003 – 2001 = 2 years
We have,
Therefore, the population in 2001 is 48,980 .
(ii) Let 
be the population in 2005 .
Given , the population in 2003 is 54,000 .
Here , P = 54000 , R = 5 % , n = 2005 – 2003 = 2 years
We have , 
Therefore, the population in 2005 is 59,535 .
11. In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000.
Solution: Here , P = 506000 , R = 2.5% and n = 2
We know that , 
Therefore, the bacteria at the end of 2 hours is 531616 (approx.)
12. A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.
Solution: Here , P = Rs 42000 , R = 8% and n = 1 year
The value of depreciation 
Therefore, the value after one year = Rs (42000 – 3360) = Rs 38,640 .
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