Question

Divide $104$ pencils among three children in the ratio $\frac{1}{2},\frac{1}{3},\frac{1}{4}.$

Answer 1

Given that there are $104$ pencils that are to be divided among three children in the ratio $\frac{1}{2},\frac{1}{3},\frac{1}{4}$.

Sum of ratio $=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}=\frac{6+4+3}{12}$

$=\frac{13}{12}$

Hence, first child will get,

$104\times \frac{\frac{1}{2}}{\frac{13}{12}}$

$=\frac{104\times 6}{13}$

$\Rightarrow \frac{624}{13}=48$

Second child will get,

$104\times \frac{\frac{1}{3}}{\frac{13}{12}}$

$=\frac{104\times 4}{13}$

$=\frac{416}{13}=32$

And third child will get,

$104\times \frac{\frac{1}{4}}{\frac{13}{12}}$

$=\frac{104\times 3}{13}$

$=\frac{312}{13}=24$

Hence, on dividing $104$ pencils among three children in the ratio $\frac{1}{2},\frac{1}{3},\frac{1}{4}$, they will get, $48,32$ and $24$ pencils respectively.