Comparing Quantities
Class 8th Mathematics CBSE Solution
- Find the ratio of the following. (a) Speed of a cycle 15 km per hour to the…
- Convert the following ratios to percentages. (a) 3 : 4 (b) 2 : 3
- 72% of 25 students are good in mathematics. How many are not good in…
- A football team won 10 matches out of the total number of matches they played.…
- If Chameli had Rs 600 left after spending 75% of her money, how much did she…
- If 60% people in a city like cricket, 30% like football and the remaining like…
- A man got a 10% increase in his salary. If his new salary is Rs. 1,54,000, find…
- On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is…
- A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16%.…
- The cost of an article was Rs 15,500. Rs 450 were spent on its repairs. If it is…
- A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on…
- During a sale, a shop offered a discount of 10% on the marked prices of all the…
- A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of…
- The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of…
- Arun bought a pair of skates at a sale where the discount given was 20%. If the…
- I purchased a hair-dryer for Rs 5,400 including 8% VAT. Find the price before…
- Calculate the amount and compound interest on (a) Rs 10,800 for 3 years at 12…
- Kamala borrowed Rs 26,400 from a Bank to buy a scooter at a rate of 15% p.a.…
- Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and…
- I borrowed Rs 12,000 from Jamshed at 6% per annum simple interest for 2 years.…
- Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compounded…
- Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per…
- Maria invested Rs 8,000 in a business. She would be paid interest at 5% per…
- Find the amount and the compound interest on Rs 10,000 for years at 10% per…
- Find the amount which Ram will get on Rs 4096, if he gave it for 18 months at 12…
- The population of a place increased to 54,000 in 2003 at a rate of 5% per annum…
- In a Laboratory, the count of bacteria in a certain experiment was increasing…
- A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per…
Exercises 8.1
Question 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
Answer:
(a)
Given that, Speed of cycle = 15 km/hr
Speed of scooter = 30 km/hr
Hence ratio of speed of cycle to that of scooter = 15 : 30 = 1 : 2
(b)
5 m : 10 km
We first need to convert terms into same unit, so 10 km = 10 x 1000 m (∵ 1 km = 1000 m)
Required ratio = 5 : (10×1000) = 1 : 2000
(c)
50 paise : Rs. 5
For finding out the ratio we need to make them in equal units
So, Rs. 5 = 5 x 100 paise
∵ 1 Rupee = 100 paise
∴ Required ratio = 50 : 500 = 1 : 10
Question 2.
Convert the following ratios to percentages.
(a) 3 : 4 (b) 2 : 3
Answer:
For converting any ratio a:b in percentage, multiply the ratio by 100.
A. 3 : 4 
= ( 3 × 25%)
= 75%
B. 2 : 3 
= 66.67 %
Question 3.
72% of 25 students are good in mathematics. How many are not good in mathematics?
Answer:
Total Number of students = 25
Given: 72% of 25 students are good in mathematics
Number of students good in mathematics = 72% x 25
Number of students who are not good in mathematics = 25 - 18
= 7
Question 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?
Answer:
Let total number of matches be x
According to question,
Win Percentage of team = 40%And team won 10 matches
So 40% of the total number of matches must be equal to 10
40% of total matches = 10
Therefore,40% of x = 10
∴ x = 25
Hence total number of matches are 25.
Question 5.
If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning?
Answer:
Let the money Chameli had at the beginning was x
According to the question,
Chameli had Rs 600 left after spending 75% of her money i.e.Money left = Money She had - 75% of Money she spent = 600
⇒ x - 75 % of x = 600
∴ Chameli had Rs. 2400 at the beginning.
Question 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 are 50 lakh, find the exact number who like each type of game.
Answer:
Per cent of the people who like other games = (100 – (60 + 30))%
= 10%
Now, number of people who like cricket = 60% of 50 lakh
Number of people who like cricket = (60/100) × 50 = 30 lakh
Number of people who like football = 30% of 50
Number of people who like football = (30/100) × 50 = 15
∴ Remaining people who like other games = 50 – 45 = 5 lakh.
Exercises 8.2
Question 1.A man got a 10% increase in his salary. If his new salary is Rs. 1,54,000, find his original salary.
Answer:
Let the original salary of the man be x,
it is given, increment in salary =10%
So new salary = old + 10% of old salary
According to the question,
New Salary = 154000
x+10% of x = 154000
⇒ x = Rs. 1,40,000
∴ His original salary was Rs. 140000.
Question 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?
Answer:
On Sunday, number of people went to the Zoo = 845
On Monday, number of people went to the Zoo = 169
∴ Decrease in number of the people = 845 – 169 = 676
Decrease percent = 
= 80%
Hence, decrease in the number of people visiting the Zoo is 80%.
Question 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.
Answer:
Given that, CP of 80 articles = Rs 2400
Also, profit% = 16%
Now after applying the profit of 16%, S.P = C.P + 16% C.P
Question 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.
Answer:
Given:
The cost of an article was Rs 15,500 and Rs 450 were spent on its repairs
∴ Total expense on the article = 15500 + 450 = Rs. 15950
To get a profit of 15%, selling price should be, S.P = 15950 + 15% of 15950
Question 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.
Answer:
Case 1: For V.C.R
Cost Price = Rs. 8000
On V.C.R, Shopkeeper made a 4% loss
So, Selling Price of V.C.R = 8000 - 4% of 8000
Case 2: T.V
Cost Price of T.V = Rs. 8000
On. T.V, shopkeeper made a profit of 8%
So, Selling Price of T.V = 8000 + 8% of 8000
Therefore,
Total C.P = 8000 + 8000 = Rs. 16000
Total S.P = 7680 + 8640 = Rs. 16320
As S.P > C.P
Profit is made by the shopkeeper.
Therefore, Profit = S.P - C.P
Profit = 16320 - 16000
Profit = Rs. 320
Question 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?
Answer:
Total Price of a pair of jeans and two shirts = 1450 + 2 × 850
= Rs 3150
And Discount = Marked Price × % Discount
Effective Price After Discount = 3150 - 315 = Rs 2835
∴ A customer have to pay Rs 2835 for a pair of jeans marked at Rs 1450 and two shirts marked at Rs 850 each
Alternate Solution:
Always remember this diagram for such questions.
This will make you remember that the discount is given on the marked price.
So 10% of Marked price is reduced from the total marked price
Thus Price after discount = 3150 - 315 = Rs. 2835
This will be the selling price of Total things bought and also the answer
Question 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)
Answer:
Given:
S.P. of each buffalo = Rs.20,000
S.P. of two buffaloes = Rs 40000
One buffalo is sold at 10% loss.
C.P. of one buffalo which i sold at a loss of 10% = 
= 
=
= Rs. 22222.22
Another buffalo is sold at 5% gain.
C.P. = 
=
=
= Rs. 19047.62
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
Question 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.
Answer: Price of T.V = Rs. 13000
Service Tax on T.V = 12 %
This Service Tax will be applied on Price of T.V
C.P of Vinod = 13000 + 12 % of 13000
Vinod will have to pay Rs. 14560 for T.V
Question 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.
Answer: Discount is offered on the Marked Price of article.
Let the marked price of article = Rs. x
It is given that the discount on pair of skates = 20%
Therefore,
Marked Price - Discount = 1600
Cross-multiplying, we get,
80x = 160000
x = Rs. 2000
Hence, the marked price of pair of skates = Rs. 2000.
Question 10.
I purchased a hair-dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added.
Answer:
C.P. = Rs.5,400 and Rate of VAT = 8%
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 = 
∴ When price including VAT is Rs.5400, then original price = 
= Rs.5000
Alternate Method: C.P including VAT = Rs. 5400, VAT = 8%
Let the amount before VAT = x
Now including VAT in X we get, CP = x + 8% of x = 5400
Thus, Price before VAT was applied was Rs. 5000
Exercises 8.3
Question 1.Calculate the amount and compound interest on
(a) Rs 10,800 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.
Answer:
Amount on Compound Interest is given by the formula,
and Compound interest can be calculated by the formula
C.I = Amount - Principal
where,
P = Principal Amount
r = rate of interest
n = time (in years)
(a) Here, Principal (P) = Rs. 10800, Time (n) = 3 years,
Rate of interest (R) = 12 1/2 % = (25/2)%
= Rs. 15,377.34
Compound Interest (C.I.) = A – P
= Rs. 15377.34 - Rs. 10800 = Rs. 4,577.34
(b) Here, Principal (P) = Rs. 18,000, Time (n) = 
years, Rate of interest (R) = 10% p.a.
[For 2 years]
= Rs. 21,780
Interest for 1/2 years on Rs. 21,780 at rate of 10% = 
= Rs. 1,089
Total amount for 
years
= Rs. 21,780 + Rs. 1089 = Rs. 22,869
Compound Interest (C.I.) = A – P
= Rs. 22869 – Rs. 18000 = Rs. 4,869
(c) Here, Principal (P) = Rs. 62500, Time (n) = 3/2 years = ½(3) years = 3 (compounded half yearly)
Rate of interest (R) = 
= 4% (compounded half yearly)
Amount (A) 
= Rs. 70,304
Compound Interest (C.I.) = A – P
= Rs. 70304 – Rs. 62500 = Rs. 7,804
(d) Here, Principal (P) = Rs. 8000, Time (n) = 2×½ years = 2(compounded half yearly)
Rate of interest (R) = half of 9% = 
(compounded half yearly)
Amount (A)
= Rs. 8,736.20
Compound Interest (C.I.) = A – P
= Rs. 8736.20 – Rs. 8000
= Rs. 736.20
(e) Here, Principal (P) = Rs. 10,000, Time (n) = 1 years = 2 years (compounded half yearly)
Rate of interest (R) = 8% = 4% (compounded half yearly)
= Rs. 10,816
Compound Interest (C.I.) = A – P
= Rs. 10,816 – Rs. 10,000 = Rs. 816
Question 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?
Answer:
Given:
Principal (P) = Rs. 26,400
Time (n) = 2 years 4 months = 2 years + 4/12 years = 7/3 years
Rate of interest (R) = 15% p.a.
**Concept: Since the interest is compounded annually so the amount for 2 years and 4 months can be calculated as finding the compound interest for 2 years and then calculating simple interest for 4 months on the amount obtained after 2 years.
Thus, the amount for 2 years (A), will be given as:
On putting the values in the formula, we get,
= 
= 
=₹ 34,914
And at the rate of 15% p.a, for time = 4 months = 
, and also the Principal will be the previous Amount obtained after 2 years = Rs. 34, 914
Simple Interest = 
= ₹ 1745.70
Therefore, the total amount = 34,914 + 1745.70 = ₹ 36,659.70
Thus, Kamala will pay Rs. 36,659.70 at the end of 2 years and 4 months to clear the loan.
Question 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?
Answer:
For Fabina Principal (P) = Rs.12,500, Time, (T) = 3 years, Rate of interest (R) = 12% p.a.
Simple Interest for Fabina = PRT/100
= Rs. 4,500
Interest paid by Fabina = Rs. 4500For Radha, P = Rs. 12,500, R = 10% and n = 3 years
= Rs. 16,637.50
So the Amount for Radha = Rs. 16637.50Now Compound Interest = Amount - Principal
∴ C.I. for Radha = A – P
= Rs. 16,637.50 – Rs. 12,500 = Rs. 4,137.50
Here, Fabina pays more interest
Difference of interests = Rs. 4,500 – Rs. 4,137.50 = Rs. 362.50
Question 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?
Answer:
Here, Principal (P) = Rs.12,000, Time (T) = 2 years, Rate of interest (R) = 6% p.a.
Simple Interest = Rs. 1,440
Had he borrowed this sum at 6% p.a., then
= Rs. 13,483.20 – Rs. 12,000
Compound Interest = Rs. 1,483.20
Difference in both interests = Rs. 1,483.20 – Rs. 1,440.00
= Rs. 43.20
Question 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?
Answer:
(i) Here, Principal (P) = Rs. 60,000,
Time, n = 6 months = 1 year(compounded half yearly)
Rate of interest (r) = 12% = 6% (compounded half yearly)
Amount (A) =
= Rs. 63,600
After 6 months Vasudevan would get amount Rs. 63,600.
(ii) Here, Principal (P) = Rs. 60,000,
Time, n = 1 year = 2 year(compounded half yearly)
Rate of interest (r) = 12% = 6% (compounded half yearly)
= Rs. 67,416
After 1 year Vasudevan would get amount Rs. 67,416
Method 2:
Principal = Rs. 60, 000, Rate of interest = 12%, Interest compounded half yearly
Rate of interest for half year = 6%
Simple interest in 6 months = p x r x t/100
Simple interest in 6 months = 60000 x 6 x 1/100
Simple Interest in 6 months = Rs. 3600
Amount at the end of 6 months = 60000 + 3600
(i) Amount at the end of 6 months = Rs. 63600
(ii) Now for next six months,
Principal = Rs. 62600. Rate of interest = 6%
Simple Interest in next 6 months = 63600 x 6 x 1/100
Amount at the end of 1 year = 63600 + 636
Amount at the end of 1 year = Rs. 64236
Question 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 
years if the interest is
(i) compounded annually.
(ii) compounded half yearly.
Answer:
(i) Interest is compounded annually
Here,
Principal (P) = Rs. 80,000, Time, n = 
years, Rate of interest (R) = 10%
We can break 1 and half year as 1 + 1/2.
So first we will calculate the Amount for 1 year
We know that the Amount is given by the formula
Now we have to calculate Amount for the left 1/2 year. For that we will use Rs. 88000 as the Principal and calculate simple Interest on this at the rate of 10%
Total amount = Rs. 88,000 + Rs. 4,400 = Rs. 92,400
(ii) Here, Principal (P) = Rs.80,000,
If the Interest is compounded Half Yearly thenTime, n = 3/2 year = 3 year (compounded half yearly)
Rate of interest (R) = 10% = 5% (compounded half yearly)
Amount is given by the formula
= Rs. 92,610
Amount when Compounded half yearly = Rs. 92610Difference in amounts
= Rs. 92,610 – Rs. 92,400 = Rs. 210
Question 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.
Answer:
(i) Here, Principal (P) = Rs. 8000, Rate of Interest (R) = 5%, Time, n = 2 years
= Rs. 8,820
Amount at the end of 2nd Year = Rs. 8,820(ii) Here, Principal (P) = Rs. 8000, Rate of Interest (R) = 5%, Time, n = 3 years
= Rs. 9,261
Interest for 3rd year = (Amount at the end of 3rd year) – (Amount at the end of 2nd year)
= Rs. 9,261 – Rs. 8,820 = Rs. 441
Question 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?
Answer:
Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10% = 5% (compounded half yearly)
Time, n = 
years = 3 years (compounded half yearly)
= Rs. 11,576.25
Compound Interest (C.I.) = A – P
= Rs. 11,576.25 – Rs. 10,000 = Rs. 1,576.25
If it is compounded annually, then
Here, Principal (P) = Rs. 10000, Rate of Interest (R) = 10%, Time 
= 
years
Amount (A) for 1 year = 
= Rs. 11,000
Interest for 1/2 year = 
= 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.
Question 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.
Answer:
Here, Principal (P) = Rs. 4096,
Rate of Interest (R) = 
(compounded half yearly)
Time, n = 18 months = years
= 3 years (compounded half yearly)
= Rs. 4,913
Question 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?
Answer:
(i)
Here, A2003 = 54,000, R = 5%, n = 2 years
Population would be less in 2001 than the population in 2003.
Here the population is increasing.
⇒ P2001 = 48,980 (approx.)
(ii) According to question, population is increasing. Therefore population in 2005,
= 59,535
Hence, population in 2005 would be 59,535.
Question 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.
Answer:
This problem can be solved on the basis of CI problems.
Let principal (P) = 5,06,000, Rate of Interest (R) = 2.5%, Time, n = 2 hours
After 2 hours, number of bacteria, =
= 5,31,616.25
Hence, number of bacteria after two hours are 531616 (approx.)
Question 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.
Answer:
Cost of scooter = Rs. 42, 000
Depreciation Rate = 8%
This means that after use, the value of the Scooter is decreasing by 8%
So for 1 year Depreciation of cost of scooter = 8% of 42000
Depreciation = Rs. 3360
So after 1 year the value of Scooter will be = Rs. 42000 - Rs. 3360 = Rs. 38640
Hence, the value of scooter after one year is Rs. 38640.