1.

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.

Answer» 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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