Exercise 8.1
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 toRs 5
(a) Speed of cycle = 15 km/hr
Speed of scooter = 30 km/hr
Hence, ratio of speed of cycle to speed of scooter = 15:30
2. Convert the following ratio to percentages
a) 3:4
b) 2:3
Solution:
a) 3:4 = ¾ = ¾ x 100% = 0.75 x 100% = 75%
b) 2:3 = 2/3 = 2/3 x 100% = 0.666 x 100% = 66.66% = 66⅔%
3. 72% of 25 students are good in mathematics. How many are not good in mathematics?
Solution:
It’s given that 72% of 25 students are good in mathematics
So, the percentage of students who are not good in mathematics = (100 – 72)%
= 28%
Here, number of students who are good in mathematics = 72/100 x 25 = 18
Thus, the number of students who are not good in mathematics = 25 – 18= 7
[Also, 28% of 25 = 28/100 x 25 = 7]
Therefore, 7 students are not good in mathematics.
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:
Let the total number of matches played by the team be x.
Given that the team won 10 matches and the winning percentage of the team was 40%.
⇒ 40/100 × x = 10
40x = 10 × 100
40x = 1000
x = 1000/40
= 100/4
= 25
Therefore, the team played 25 matches.
5. If Chameli had ₹600 left after spending 75% of her money, how much did she have in the beginning?
Solution:
Let the amount of money which Chameli had in the beginning be x
Given that, after spending 75% of ₹x, she was left with ₹600
So, (100 – 75)% of x = ₹600
Or, 25% of x = ₹600
25/100 × x = ₹600
x = ₹600 × 4
= ₹2400
Therefore, Chameli had ₹2400 is the beginning.
6. If 60% people in 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.
Solution:
Percentage of people who like other games = (100 – 60 – 30)%
= (100 – 90)%
= 10%
Total number of people = 50 lakhs
So,
Number of people who like cricket = 60/100 x 50 = 30 lakhs
Number of people who like football = 30/100 x 50 = 15 lakhs
Number of people who like other games = 10/100 x 50 = 5 lakhs
Exercise 8.2
1. A man got a 10% increase in his salary. If his new salary is ₹1,54,000, find his original salary.
Solution:
Let the original salary be x
Given that, the new salary is ₹1,54,000
Original salary + Increment = New salary
Given that the increment is 10% of the original salary
So, (x + 10/100 × x) = 154000
x + x/10 = 154000
11x/10 = 154000
x = 154000 × 10/11
= 140000
Therefore, the original salary was ₹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 that on Sunday, 845 people went to the zoo and on Monday, 169 people went to the zoo
Decrease in the number of people = 845 – 169 = 676
Thus,
Percentage decrease = (Decrease in the number of people/Number of people who went to zoo on Sunday) x 100%
= (676/845 x 100)%
= 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.
Solution:
Given that the shopkeeper buys 80 articles for ₹ 2,400
Cost of one article = 2400/80 = ₹ 30
Profit percentage = 16%
Profit percentage = Profit/C.P x 100
16 = Profit/30 x 100
Profit = (16 x 30)/100
= ₹ 4.8
Therefore, selling price of one article = C.P + Profit
= ₹ (30 + 4.80)
= ₹ 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.
Solution:
Total cost of an article = Cost + Overhead expenses
= ₹15500 + ₹450
= ₹15950
Profit percentage = 15%
Profit percentage = Profit/C.P x 100
15 = Profit/15950 x 100
Profit = (15 x 15950)/100
= 2392.50
Therefore, Selling price of the article = C.P + Profit
= ₹(15950 + 2392.50)
= ₹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 percent on the whole transaction.
Solution:
C.P. of a VCR = ₹ 8000
The shopkeeper made a loss of 4 % on VCR
This means if C.P. is ₹ 100, then S.P. is ₹ 96. When C.P. is ₹ 8000
S.P. = (96/100 x 8000) = ₹ 7680
C.P. of a TV = ₹ 8000
The shopkeeper made a profit of 8 % on TV.
This means that if C.P. is ₹ 100, then S.P. is ₹ 108.
When C.P. is ₹ 8000,
S.P. = (108/100 x 8000) = ₹ 8640
Total S.P. = ₹ 7680 + ₹ 8640 = ₹ 16320
Total C.P. = ₹ 8000 + ₹ 8000 = ₹ 16000
Since, total S.P.> total C.P. ⇒ profit
Profit = ₹ 16320 − ₹ 16000 = ₹ 320
Therefore, the shopkeeper had a gain of 2% 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?
Solution:
Total marked price = ₹ (1,450 + 2 × 850)
= ₹ (1,450 +1,700)
= ₹ 3,150
Given that, discount percentage = 10%
Discount = ₹ (10/100 x 3150) = ₹ 315
Also, Discount = Marked price − Sale price
₹ 315 = ₹ 3150 − Sale price
∴ Sale price = ₹ (3150 − 315)
= ₹ 2835
Therefore, 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)
Solution:
S.P. of each buffalo = ₹ 20,000
The milkman made a gain of 5% while selling one buffalo
This means if C.P. is ₹ 100, then S.P. is ₹ 105.
C.P. of one buffalo = 100/105 × 20000
= ₹ 19,047.62
Also, the second buffalo was sold at a loss of 10%
This means if C.P. is ₹ 100, then S.P. is ₹ 90
∴ C.P. of other buffalo = 100/90 × 2000
= ₹ 22222.22
Total C.P. = ₹ 19047.62 + ₹ 22222.22 = ₹ 41269.84
Total S.P. = ₹ 20000 + ₹ 20000 = ₹ 40000
Loss = ₹ 41269.84 − ₹ 40000 = ₹ 1269.84
Therefore, the overall loss of milkman was ₹ 1,269.84
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,
Solution:
On ₹ 100, the tax to be paid = ₹ 12
Here, on ₹ 13000, the tax to be paid will be = 12/100 × 13000
= ₹ 1560
Required amount = Cost + Sales Tax
= ₹ 13000 + ₹ 1560
= ₹ 14560
Therefore, Vinod will have to pay ₹ 14,560 for the T.V.
9. Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1,600, find the marked price.
Solution:
Let the marked price be x
Discount percent = Discount/Marked Price x 100
20 = Discount/x × 100
Discount = 20/100 × x
= x/5
Also,
Discount = Marked price – Sale price
x/5 = x – ₹ 1600
x – x/5 = 1600
4x/5 = 1600
x = 1600 x 5/4
= 2000
Therefore, the marked price was ₹ 2000.
10. I purchased a hair-dryer for ₹ 5,400 including 8% VAT. Find the price before VAT was added.
Solution:
The price includes VAT
So, 8% VAT means that if the price without VAT is ₹ 100,
then price including VAT will be ₹ 108
When price including VAT is ₹ 108, original price = ₹ 100
When price including VAT is ₹ 5400, original price = ₹ (100/108 × 5400)
= ₹ 5000
Therefore, the price of the hair-dryer before the addition of VAT was ₹ 5,000.
Exercise 8.3
1. Calculate the amount and compound interest on
(a) ₹ 10,800 for 3 years at 12½ % per annum compounded annually.
Solution:
Principal (P) = ₹ 10,800
Rate (R) = 12½ % = 25/2 % (annual)
Number of years (n) = 3
Amount (A) = P(1 + R/100)n
= 10800(1 + 25/200)3
= 10800(225/200)3
= 15377.34375
= ₹ 15377.34 (approximately)
C.I. = A – P
= ₹ (15377.34 – 10800)
= ₹ 4,577.34
(b) ₹ 18000 for 2½ years at 10% per annum compounded annually.
Solution:
Principal (P) = ₹ 18,000
Rate (R) = 10% annual
Number of years (n) = 2½
The amount for 2 years and 6 months can be calculated by calculating the amount for 2 years
using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 2 years
First, the amount for 2 years has to be calculated
Amount, A = P(1 + R/100)n
= 18000(1 + 1/10)2
= 1800(11/10)2
= ₹ 21780
By taking ₹ 21780 as principal, the S.I. for the next ½ year will be calculated
S.I. = (21780 x ½ x 10)/100
= ₹ 1089
Hence, the interest for the first 2 years = ₹ (21780 – 18000) = ₹ 3780
And, interest for the next ½ year = ₹ 1089
Total C.I. = ₹ 3780 + ₹ 1089
= ₹ 4,869
Therefore,
Amount, A = P + C.I.
= ₹ 18000 + ₹ 4869
= ₹ 22,869
(c) ₹ 62500 for 1½ years at 8% per annum compounded half yearly.
Solution:
Principal (P) = ₹ 62,500
Rate = 8% per annum or 4% per half year
Number of years = 1½
There will be 3 half years in 1½ years
Amount, A = P(1 + R/100)n
= 62500(1 + 4/100)3
= 62500(104/100)3
= 62500(26/25)3
= ₹ 70304
C.I. = A – P = ₹ 70304 – ₹ 62500 = ₹ 7,804
(d) ₹ 8000 for 1 year at 9% per annum compound half yearly.
(You could use the year by year calculation using SI formula to verify)
Solution:
Principal (P) = ₹ 8000
Rate of interest = 9% per annum or 9/2% per half year
Number of years = 1 year
There will be 2 half years in 1 year
Amount, A = P(1 + R/100)n
= 8000(1 + 9/200)2
= 8000(209/200)2
= 8736.20
C.I. = A – P = ₹ 8736.20 – ₹ 8000 = ₹ 736.20
(e) ₹ 10000 for 1 year at 8% per annum compounded half yearly.
Solution:
Principal (P) = ₹ 10,000
Rate = 8% per annum or 4% per half year
Number of years = 1 year
There are 2 half years in 1 year
Amount, A = P(1 + R/100)n
= 10000(1 + 4/100)2
= 10000(1 + 1/25)2
= 10000(26/25)2
= ₹ 10816
C.I. = A – P = ₹ 10816 – ₹ 10000 = ₹ 816
2. Kamala borrowed ₹ 26400