NCERT Solutions Class 8 Mathematics Chapter 8 Comparing Quantities

Exercise 8.1

Q.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) 50 m to 10 km
(c) 50 paise to Rs.5
Sol.1) (a) Speed of cycle = 15 𝑘𝑚/ℎ𝑟
Speed of scooter = 30 𝑘𝑚/ℎ𝑟
Hence ratio of speed of cycle to that of scooter = 15 ∶ 30
= 15/30 = 1/2 = 1: 2

(b) 1 𝑘𝑚 = 1000 𝑚
∴ 10 𝑘𝑚 = 10 × 1000 = 10000 𝑚
∴ Ratio = 5 𝑚/10000 𝑚 = 1/2000 = 1 ∶ 2000

(c) Rs.1 = 100 paise
∴ Rs.5 = 5 × 100 = 500 𝑝𝑎𝑖𝑠𝑒
Hence Ratio = 50 𝑝𝑎𝑖𝑠𝑒/500 𝑝𝑎𝑖𝑠𝑒 = 1/10 = 1 ∶ 10

Q.2) Convert the following ratios to percentages: (a) 3 : 4 (b) 2 : 3
Sol.2) (a) Percentage of 3 ∶ 4 = 3/4 × 100 % = 75%
(b) Percentage of 2 ∶ 3 = 2/3 × 100 % = 66(2/3)%

Q.3) 72% of 25 students are good in mathematics. How many are not good in mathematics?
Sol.3) Total number of students = 25
Number of good students in mathematics = 72% 𝑜𝑓 25 = 72/100 × 25 = 18
Number of students not good in mathematics = 25 – 18 = 7
Hence percentage of students not good in mathematics = 7/25 × 100 = 28%

Q.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?
Sol.4) Let total number of matches be 𝑥
According to question,
40% of total matches = 10
⇒ 40% of 𝑥 = 10
⇒ 40/100 × 𝑥 = 10
⇒ 𝑥 = 10×100/40 = 25
Hence total number of matches is 25.

Q.5) If Chameli had Rs. 600 left after spending 75% of her money, how much did she have in the beginning?
Sol.5) Let her money in the beginning be 𝑅𝑠. 𝑥
According to question,
𝑥 − 75% 𝑜𝑓 𝑥 = 600

⇒𝑥 = 600 × 4 = 𝑅𝑠. 2400
Hence the money in the beginning was 𝑅𝑠. 2400

Q.6) If 60% people in a city like cricket, 30% like football and the remaining like other games, then what percent 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.
Sol.6) Number of people who like cricket = 60%
Number of people who like football = 30%
Number of people who like other games = 100% – (60% + 30%) = 10%
Now Number of people who like cricket = 60% of 50,00,000
= 60/100 × 50,00,000 = 30,00,000
And Number of people who like football = 30% of 50,00,000
= 30/100 × 50,00,000 = 15,00,000
∴ Number of people who like other games = 10% of 50,00,000
= 10/100 × 50,00,000 = 5,00,000
Hence, numbers of people who like other games are 5 lakh.

Exercise 8.2

Q.1) A man got 10% increase in his salary. If his new salary is Rs.1,54,000, find his original salary.
Sol.1) Let original salary be Rs.100.
Therefore, New salary i.e., 10% increase = 100 + 10 = Rs. 110
New salary is Rs.110, when original salary = Rs.100
∴ New salary is Rs.1, when original salary = 100/110
∴ New salary is Rs.1,54,000, when original salary = 100/110
× 154000 = 𝑅𝑠. 1,40,000
Hence original salary is 𝑅𝑠. 1,40,000.

Q.2) On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the percent decrease in the people visiting the Zoo on Monday?
Sol.2) On Sunday, people went to the Zoo = 845
On Monday, people went to the Zoo = 169
Number of decrease in the people = 845 – 169 = 676
Decrease percent = 676/845 × 100 = 80%
Hence decrease in the people visiting the Zoo is 80%.

Q.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.
No. of articles = 80
Cost Price of articles = Rs. 2,400
And Profit = 16%
Cost price of articles is Rs.100,
then selling price = 100 + 16 = Rs.116
∴ Cost price of articles is Rs.1,
then selling price = 116/100
∴ Cost price of articles is Rs.2400,
then selling price = 116/100 × 2400 = 𝑅𝑠. 2784
Hence, Selling Price of 80 articles = Rs.2784
Therefore Selling Price of 1 article = 2784/80 = 𝑅𝑠. 34.80

Q.4) The cost of an article was Rs.15,500, Rs.450 were spent on its repairs. If it sold for a profit of 15%, find the selling price of the article.
Sol.4) Here, C.P. = Rs.15,500 and
Repair cost =Rs. 450
Therefore, Total Cost Price = 15500 + 450 = Rs.15,950
Let C.P be Rs. 100, then S.P. = 100 + 15 = Rs. 115
When C.P. is Rs.100, then S.P. = Rs.115
∴ When C.P. is Rs. 1, then S.P. = 115/100
∴ When C.P. is Rs.15950, 
then S.P. 115/100 × 15950 = 𝑅𝑠. 18,342.50

Q.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.
Sol.5) Cost price of VCR = 𝑅𝑠. 8000 and
Cost price of TV = 𝑅𝑠. 8000
Total Cost Price of both articles = 𝑅𝑠. 8000 + 𝑅𝑠. 8000 = 𝑅𝑠. 16,000
Now VCR is sold at 4% loss. Let C.P. of each article be Rs. 100,
then S.P. of VCR = 100 – 4 = Rs. 96 When C.P. is Rs. 100, then S.P. = Rs. 96
∴ When C.P. is Rs. 1, then S.P. = 96/100
∴ When C.P. is 𝑅𝑠. 8000, then S.P. = 96/100 × 8000 = 𝑅𝑠. 7,680
And TV is sold at 8% profit, then S.P. of TV = 100 + 8 = Rs. 108
When C.P. is Rs. 100, then S.P. = Rs. 108
∴ When C.P. is Rs. 1, then S.P. = 108/100
∴ When C.P. is Rs. 8000, then S.P. =  108/100 × 8000 = 𝑅𝑠. 8,640
Then, Total S.P. = Rs. 7,680 + Rs. 8,640 = Rs. 16,320
Since S.P. > C.P.,
Therefore Profit = S.P. – C.P. = 16320 – 16000 = Rs.320 And
Profit% = 𝑃𝑟𝑜𝑓𝑖𝑡/𝐶𝑜𝑠𝑡 𝑃𝑟𝑖𝑐𝑒 × 100 = 320/16000 × 100 = 2%

Q.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?
Sol.6) Rate of discount on all items = 10%
Marked Price of a pair of jeans = 𝑅𝑠. 1450 and
Marked Price of a shirt = 𝑅𝑠. 850

∴ S.P. of two shirts = Rs. 1700 – Rs. 170 = Rs. 1530
Therefore, the customer had to pay = 1305 + 1530 = Rs. 2,835

Q.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)
Sol.7) S.P. of each buffalo = 𝑅𝑠. 20,000
S.P. of two buffaloes = 𝑅𝑠. 20,000 × 2 = 𝑅𝑠. 40,000
One buffalo is sold at 5% gain.
Let C.P. be Rs. 100,
then S.P. = 100 + 5 = Rs.105
When S.P. is Rs. 105, then C.P. = Rs. 100
∴ When S.P. is Rs. 1, then C.P. = 100/105
∴ When S.P. is Rs. 20,000, then C.P. = 100/105 × 20,000 = 𝑅𝑠. 19,047.62
Another buffalo is sold at 10% loss.
Let C.P. be Rs. 100,
then S.P. = 100 – 10 = Rs. 90
When S.P. is Rs. 90, then C.P. = Rs. 100
∴ When S.P. is Rs. 1, then C.P. = 100 90
∴ When S.P. is Rs. 20,000, then C.P = 100/90 × 20,000 = 𝑅𝑠. 22,222.22
Total C.P. = Rs. 19,047.62 + Rs. 22,222.22 = Rs. 41,269.84
Since C.P. > S.P.
Therefore, here it is loss. Loss = C.P. – S.P.
= Rs. 41,269.84 – Rs. 40,000.00 = Rs. 1,269.84

Q.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.
Sol.8) C.P. = Rs. 13,000 and
S.T. rate = 12%
Let C.P. be Rs. 100,
then S.P. for purchaser = 100 + 12 = Rs. 112
When C.P. is Rs. 100, then S.P. = Rs. 112
∴ When C.P. is Rs. 1, then S.P. = 112/100
∴ When C.P. is Rs. 13,000,
then S.P. = 112/100 × 13000 = 𝑅𝑠. 14,560

Q.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.
Sol.9) S.P. = Rs.1,600 and
Rate of discount = 20%
Let M.P. be Rs. 100, then S.P. for customer = 100 – 20 = Rs. 80
When S.P. is Rs. 80, then M.P. = Rs. 100
∴ When S.P. is Rs.1, then M.P. = 100/80
When S.P. is Rs.1600, then M.P. = 100/80 × 1600 = 𝑅𝑠. 2,000

Q.10) I purchased a hair-dryer for Rs. 5,400 including 8% VAT. Find the price before VAT was added.
Sol.10) Let C.P. without VAT is Rs.100,
then price including VAT = 100 + 8 = Rs. 108
When price including VAT is Rs. 108, then original price = Rs. 100
∴ When price including VAT is Rs. 1, then original price = 100/108
∴ When price including VAT is Rs. 5400, then original price = 100/108 × 5400 = 𝑅𝑠. 5000

Exercise 8.3

Q.1) Calculate the amount and compound interest on:
(a) Rs. 10,800 for 3 years at 12(1/2)% 2 per annum compounded annually.
(b) Rs. 18,000 for 2(1/2)years at 10% per annum compounded annually.
(c) Rs. 62,500 for 1(1/2)years at 8% per annum compounded annually.
(d) Rs. 8,000 for 1 years at 9% per annum compounded half yearly.
(You could the year by year calculation using S.I. formula to verify).
(e) Rs. 10,000 for 1 years at 8% per annum compounded half yearly
Sol.1) (a) Here, Principal (P) = Rs. 10800, Time (n) = 3 years,

Q.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?
Sol.2) Here, Principal (P) = Rs. 26,400, Time (n) = 2 years 4 months, Rate of interest (R) = 15% p.a.

Q.3) Fabina borrows Rs. 12,500 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?
Sol.3) Here, Principal (P) = Rs. 12,500, Time (T) = 3 years, Rate of interest (R) = 12% p.a.

= 𝑅𝑠. 16,637.50
∴ C.I. for Radha = A – P = Rs. 16,637.50 – Rs. 12,500 = Rs. 4,137.50
Here, Fabina pays more interest = Rs. 4,500 – Rs. 4,137.50 = Rs. 362.50

Q.4) I borrows 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?
Sol.4) Here, Principal (P) = Rs.12,000, Time (T) = 2 years, Rate of interest (R) = 6% p.a.

Difference in both interests = 𝑅𝑠. 1,483.20 – 𝑅𝑠. 1,440.00 = 𝑅𝑠. 43.20

Q.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?
Sol.5) i) Here, Principal (P) = 𝑅𝑠. 60,000
Time (n) = 6 months = 1 half-year (compounded half yearly)
Rate of interest (R) = 12% = 6% (compounded half yearly)

Q.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 1(1/2) years if the interest is:
i) compounded annually. (ii) compounded half yearly
Sol.6) (i) Here, Principal (P) = Rs. 80,000, Time (n) = 1 1 2 years,
Rate of interest (R) = 10%

Q.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 third year.
Sol.7) (i) Here, Principal (P) = Rs. 8000, Rate of Interest (R) = 5%, Time (n) = 2 years

Q.8) Find the amount and the compound interest on Rs. 10,000 for 1(1/2) years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
Sol.8) Here, Principal (P) = 𝑅𝑠. 10000, Rate of Interest (R) = 10% = 5% (compounded half yearly)
Time (n) = 1(1/2) years = 3 half-years                                                       (compounded half yearly)

Interest for 1/2 year = 11000×1×10/2×100 = 𝑅𝑠. 550
∴ Total amount = 𝑅𝑠. 11,000 + 𝑅𝑠. 550 = 𝑅𝑠. 11,550
Now, C.I. = 𝐴 – 𝑃 = 𝑅𝑠. 11,550 – 𝑅𝑠. 10,000 = 𝑅𝑠. 1,550
Yes, interest 𝑅𝑠. 1,576.25 is more than 𝑅𝑠. 1,550.

Q.9) Find the amount which Ram will get on Rs. 4,096, if he gave it for 18 months at 12(1/2)% per annum, interest being compounded half yearly.
Sol.9) Here, Principal (P) = 𝑅𝑠. 4096,

Q.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?
Sol.10) (i) Here, 𝐴2003 = 54,000, 𝑅 = 5%, 𝑛 = 2 𝑦𝑒𝑎𝑟𝑠
Population would be less in 2001 than 2003 in two years. Here population is increasing.

Q.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.
Sol.11) Here, Principal (P) = 5,06,000, Rate of Interest (R) = 2.5%, Time (n) = 2 hours
After 2 hours, number of bacteria,

Hence, number of bacteria after two hours are 531616 (approx.).

Q.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.
Sol.12) Here, Principal (P) = Rs. 42,000, Rate of Interest (R) = 8%, Time (n) = 1 years