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The average scored by the students of a ...

The average scored by the students of a class in English is `64.` The average of marks scored by boys and the girls are respectively `68` and `58.` Then find the ratio of the number of boys to the number of girls.

Text Solution

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Let `n_(1)` boys and `n_(2)` girls are there in a class
Average marks of boys `=68`
`rArr "Sum of marks of all the boys" = 68n_(1) " " (sumx_(i) = n bar(x))`
Similarly,
Sum of marks of all the girls `=58n_(2) " " (sumx_(i) = n bar(x))`
`therefore "Sum of marks of all students " = 68n_(1) + 58n_(2)`
`therefore " Average marks" = (68n_(1) + 58n_(2))/(n_(1)+n_(2))= 64 " " `(given)
`rArr 68n_(1) + 58n_(2) = 64n_(1)+64n_(2)`
`rArr 4n_(1) = 6n_(2) rArr (n_(1))/(n_(2))=(6)/(4)=(3)/(2)`
`therefore "Required ratio " = 3:2`
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