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 ? 5
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
(a)Given, Speed of cycle : Speed of Scooter = 15 km per hour : 30 km per hour
Hence we get the ratio as 1 : 2
(b)Given, 5 m to 10 km
Hence, the ratio = 1 : 2000
(c)Given, 50 paise to ? 5
Hence we get the ratio as 1 : 10
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?
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Win percentage is 40 i.e. 40 matches are won by the team out of 100 matches
So, the team will win 1 match out of
And similarly, the team will win 10 matches out of
Hence, the total number of matches played by the team = 25
5. If Chameli had ? 600 left after spending 75% of her money, how much did she have in the beginning?
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Let the money with Chameli be ? 100
So, the money spent by her = 75% of 100
The money left with her = ? 100 – ?75 = ? 25
? 25 are left with her out of ? 100
? 1 is left with her out of ?
Similarly, ? 600 will be left out of ?
Thus, she had ? 2400 in beginning.
6.If 60% of people in a city like a 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.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Total number of people = 50,00,000
We have the number of people who like cricket = 60% of 50,00,000
Similarly we have the number of people who like football = 30% of 50,00,000
Hence, the number of people who like other games = 50,00,000 – (30,00,000 + 15,00,000)
So,the number of people who likes other games=5,00,000 and the percentage of the people who like other games =
Thus, 10% of people like other game.
1.A man got a 10% increase in his salary. If his new salary is ? 1,54,000, find his original salary.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
New salary of the man= ? 1,54,000
Given, the increase in salary = 10%
New salary of the man = Original salary
Thus, the original salary = ? 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?
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Given, Number of people went to Zoo on Sunday = 845
Number of people went to Zoo on Monday = 169
So the decrease in number of people visiting the Zoo = 845 – 169 = 676
Hence we have the decrease in percent:
Hence we have the decrease in per cent of visiting people= 80%
3.A shopkeeper buys 80 articles for ? 2,400 and sells them for a profit of 16%. Find the selling price of one article.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
We have Cost price of 80 articles = ? 2,400
So, Cost of 1 article = ?
Given Profit = 16%
So, we know
Hence, the selling price of one article =? 34.80
4.The cost of an article was ? 15,500. ? 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Given, CP of the article = ? 15,500
The money spent on repairs = ? 450
So we have the net CP = ? 15,500 +? 450 = ? 15,950
Given that Profit = 15%
So, we know
Hence, the selling price of article = ? 18342.50
5.A VCR and TV were bought for ? 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 per cent on the whole transaction.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Given, Cost price of VCR=? 8,000.
And Loss=4%
?
Also given that, Cost price of TV=? 8,000
And profit=8%
?
So we have total SP=? 8,640 +? 7,680=? 16,320
So we have total SP=? 8000 + ? 8000 =? 16,000
Therefore, Profit=SP-CP
=? 16,320- ? 16,000
=? 320
? Profit % on the whole transaction=
Hence, the shopkeeper gained 2% profit 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 ? 1450 and two shirts marked at ? 850 each?
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Marked Price(MP) of Jeans = ? 1,450
Marked Price of two shirts = ? 850
Total Marked Price = ? 1,450 + ? 1,700 = ? 3,150
Given that we have discount = 10%
So, we know
Thus, the customer will have to pay ? 2,835.
7.A milkman sold two of his buffaloes for ? 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]
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Given, SP of a buffalo=? 20,000.
And Gain=5%
?
SP of another buffalo=? 20,000
And given loss=10%
?
So we have total CP=
And we have total SP=? 20,000 + ? 20,000 =? 40,000
Here we see that,SP < CP i.e., it was a loss.
? Loss=CP-SP
Therefore, %Loss=
=
=
=
Hence, the complete percent loss=
8.The price of a TV is ? 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.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Marked price of TV = ? 13000
Given that the Rate of sales tax = 12%
? Sales tax = 12% of ? 13000
So, the total amount which Vinod had to pay for purchasing TV = ? (13000 +1560) = ? 14560.
Hence, The required amount that Vinod has to pay = ? 14,560
9. Arun bought a pair of skates at a sale where the discount is given was 20%. If the amount he pays is ? 1,600, find the marked price.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Let the marked price of the skates be ? 100
We are given discount = ? 20% of 100 = ? 20
So the Sale price =? 100 – ? 20 = ? 80
If SP is ? 80 then marked price =? 100
so,if SP is ? 1 then marked price = ?
Similarly, if SP is ? 1,600 then marked price = ?
Hence, we got the marked price = ? 2000.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
Let the original price of the hair-dryer be ? 100
Given, VAT = 8% of 100 = ? 8
So, the Sale price = ? 100 + ? 8 = ? 108
If SP is ? 108 then original price =? 100
So, if SP is ? 1 then the original price = ?
Similarly, if SP is ? 5,400 then the original price = ?
Thus, the price of hair-dryer before the addition of VAT = ? 5000.
1. Calculate the amount and compound interest on
(a)? 10,800 for 3 years at
(b)? 18,000 for
(c)? 62,500 for
(d) ? 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)? 10,000 for 1 year at 8% per annum compounded half yearly.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
(a) Given, P=? 10,800,n=3 years.
We have, R=
So, we know that
Thus, we have Compound interest=A - P
=? 15,377.34-? 10,800 = ? 4,577.35
Hence we have, amount = ? 15,377.34 and CI = ? 4,577.34
(b)We have: P = ? 18,000, n =
The amount for
The amount for 2 years:
Amount =
=
=
? Interest after 2 years = Amount - P
=21,780-18,000=? 3,780
So, now taking principal amount as ? 21,780, the SI for the next
SI=
=
=
Therefore,Total CI = ? 3780 +? 1,089= ? 4,869
Amount = P + I = ? 21,780 + ? 1,089 =? 22,869
Hence, the amount = ? 22,869 and CI = ? 4,869
(c)Given, P=? 62,500,n=
We have, R=
So, we know that
Thus, we have Compound interest=A - P
=? 70,304-? 62,500 = ? 7,804
Hence we have, amount = ? 70,304 and CI = ? 7804
(d)Given, P=? 8,000,n=1 years and R = 9% per annum compounded half yearly
Since, the interest is compounded half yearly n =
So, we know that
Thus, we have Compound interest=A - P
=? 8,736.20-? 8,000 = ? 736.20
Hence we have, amount = ? 8736.20 and CI = ? 736.20
(e)Given, P=? 10,000,n=1 years and R = 8% per annum compounded half yearly
Since, the interest is compounded half yearly n =
So, we know that
Thus, we have Compound interest=A - P
=? 10,816 -? 10,000 = ? 816
Hence we have, amount = ? 10,816 and CI = ? 816
2.Kamala borrowed ? 26,400 from a Bank to buy a scooter at a rate of 15% per annum compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? (Hint: Find amount for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
We have:
P = ? 26,400
R = 15% p.a. compounded yearly
n = 2 years and 4 months
So, amount for 2 years=
=
=
=
=
Principal for 2 years=? 34,914
So, SI for 4 months =
=
=
Thus, the mount after 2 years and 4 months = ? 34,914 + ? 1745.70 = ? 36,659.70
Hence, the total amount to be paid by Kamla = ? 36,659.70
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?
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
We have given data for Fabina as: P = ? 12,500, R = 12% p.a. and n = 3 years
So, SI for 4 months =
=
=
Therefore we have, CI=A - P
=
=
=
=
=
=
=
=
=
So, the difference between the two interests = ? 4500 – ? 4137.50 = ? 362.50
Hence, Fabina pays more interest by ? 362.50.
I borrowed ? 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?
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
We have given data : P = ? 12,000, R = 6% p.a. and n = 2 years
So, SI for 4 months =
=
=
Therefore we have, CI=A - P
=
=
=
=
=
=
=
=
=
So, the difference between the two interests = ? 1483.20 – ? 1440 = ? 43.20
Hence, Fabina pays more interest by ? 43.20.
5.Vasudevan invested ? 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?
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
(i) Given: P = ? 60,000, R = 12% p.a. compounded half yearly and n=6 months=
? Simple Interest=
=
=
Therefore , we have Amount=P+SI
=? 60,000 + ? 3600
=? 63600
So the required amount =? 63600
(ii)We have given with :P = ? 60,000, R =
So, we have amount=
=
=
=
=
Hence the required amount= ? 67,416
6. Arif took a loan of ? 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after
(i) compounded annually.
(ii) compounded half yearly.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
(i) We are given: P = ? 80,000 , R = 10% p.a. and n =
Simple Interest=
=
=
Principal for the second year=P+SI
=? 80,000 + ? 8,000 = ? 88,000
Now for
Thus, amount=? 88,000 + ? 4,400=? 92,400
(ii)So for compounded interest half yearly we have:
R=
n=
? Amount=
=
=
=
=
=
Difference between the amounts = ? 92,610 – ? 92,400 = ? 210
7.Maria invested ? 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.
NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities
Answer :
(i) Given: P = ? 8,000, R = 5% p.a. and n = 2 years
Amount=
=
=
=
=
=
Thus, the amount credited at the end of 2 years=? 8,820
(ii) Interest for the third year=Amount after 3 years - Amount after 2 years
=
=
=
=