Page 174 - Start Up Mathematics_8 (Non CCE)

Example 11: The price of sugar has been increased by 40%. By how much percent must this new price be
decreased to retain its former price?
Solution: Let the original price of sugar be ` 100.
Increase in price = 40% of ` 100 = ` 40

New price = ` (100 + 40) = ` 140
In order to retain the original price, reduction needed = ` (140 – 100) = ` 40
Reduction needed on ` 140 = ` 40
Ê 40 ˆ
Reduction needed on ` 1 = ` Á Ë 140¯ ˜

40
ˆ
Reduction needed on ` 100 = ` Ê 140 ¥ 100 = ` 28 4
Á
˜
Ë
¯
7
4
\ the new price of sugar should be reduced by 28 % to retain the original price.
7
Example 12: Find the percentage of pure gold in 18-carat gold, if 24-carat gold is hundred percent pure gold.
Solution: In 18-carat gold, pure gold is 18 parts out of 24 parts.
Ê 18 ˆ
\ percentage of pure gold in 18-carat gold = Á Ë 24 ¥ 100 % = 75%
˜
¯
EXERCISE 11.2

1. Find:
1
(a) 24% of 110 (b) 12 % of ` 250 (c) 60% of 700 g (d) 2.5% of 10,000 mL
2. What percent is: 2
1
(a) 20 of 50? (b) 400 g of 4 kg? (c) ` 6.50 of ` 5? (d) 2 of ?
3. Find the number x if: 3 9
(a) 6% of x is 42 (b) 10% of x is 35 (c) 150% of x is 300 (d) 0.5% of x is 45
4. a is 5% of b, b is 24% of c. If a = 480, find the values of b and c.
5. Hariti got 85% marks in her first term examination and 76% marks in her final examination. In the first
term examination, the maximum marks were 1,200 and in the final examination, the maximum marks
were 1,500. What is the percentage of marks obtained by Hariti considering both the examinations
simultaneously?
6. The price of rice is increased by 10%. If the new price is ` 50 per kg, find the old price.
7. A cricketer hits 120 runs in 150 balls during a test match. 20% of the runs came in 6s, 30% in 4s,
25% in 2s and the rest in 1s. How many runs did he score in:
(a) 6s (b) 4s (c) 2s (d) 1s
8. An alloy of copper and tin consists of 20 parts of tin and 108 parts of copper. Find the percentage of
tin and of copper in the alloy.
9. 40% of the passengers from a train got down at station X, 75% of the remaining got down at station
Y. If the remaining 12 were taken to station Z, how many passengers were there in the train?
10. The population of a city increases by 10% annually. If the present population is 65,000, what will be
its population after 2 years?
11. In a school, 60% students like orange juice, 30% like mango juice and the remaining like grape juice.
What percent of students like grape juice? If the total number of students in the school is 2,500, find
the exact number of students who like each type of juice.

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