Question

Divide 282 into two parts such that the eighth part of the first and the fifth part of the second are in the ratio 4 : 3 are 192 and 90
If true then enter $1$ and if false then enter $0$

Answer 1

Let 282 be divided into parts, $a$ and $282-a$
Given, eighth part of the first and the fifth part of the second are in the ratio $4:3$
=> $\frac{\frac{a}{8}}{\frac{282-a}{5}}=\frac{4}{3}$
=> $\frac{5a}{2256-8a}=\frac{4}{3}$
Cross-multiplying, $3\times 5a=4\times (2256-8a)$
$15a=9024-32a$
$47a=9024$
$a=192$
and $282-192=90$
Thus the required parts of $282$ are $192,90$