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The average marks of boys in a class is ...

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

A

80

B

60

C

40

D

20

Text Solution

Verified by Experts

The correct Answer is:
A
Let `n_(1) and n_(2)` be the number of boys and girls respectively in the class.

We have, `bar(X_(1))=52,bar(X_(2))=42 and bar(X) =50`
`therefore bar(X)=(n_(1)bar(X_(1))+n_(2)bar(X_(2)))/(n_(1)+n_(2))`
`rArr 50=(52n_(1)+42n_(2))/(n_(1)+n_(2)) rArr 8n_(2)=2n_(1) rArr n_(1)=4n_(2)`
`therefore " Percentage of boys "=(n_(1))/(n_(1)+n_(2)) xx 100=(4n_(2))/(5n_(2)) xx 100=80`
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