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The average of marks scored by the students of a class is 68. The average of marks of the girls in the class is 80 and that of boys is 60. What is the percentage of boys in the class ?
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- 40 %
- 60 %
- 65 %
- 70 %
- 40 %
Correct Option: B
Let the number of boys and girls in the class be p and q respectively.
∴ 60p + 80q = 68(p + q)
⇒ 60p + 80q = 68p + 68q
⇒ 8p = 12q
⇒ 2p = 3q ⇒ q = 2 / 3p
| ∴ Required percentage = | p | × 100 |
| p + q |
| Required percentage = | × 100 | ||||
| p + | p | ||||
| 3 | |||||
| Required percentage = | 3p | × 100 |
| 3p + 2q |
| Required percentage = | 3 | × 100 = 60% |
| 5 |
Second method to find the required percentage : By Alligation method
According to the question,
Ratio of girls to boys = 8 : 12 = 2 : 3
| ∴ Percentage of boys = | 3 | × 100 = 60% |
| 5 |
