Question

Divide $1162$ into three parts such that $4$ times the first part, $5$ times the second part and $7$ times the third part are equal.

• A. $490,392,280$
• B. $492,392,380$
• C. $493,329,389$
• D. $393,290,360$

Answer 1

Answer: (A)

$490,392,280$

We have, $4\times$ first part $=5\times$ second part
$=7\times$ third part $=$x(say)
According to question,
$\frac{x}{4}+\frac{x}{5}+\frac{x}{7}=1162$
$\Rightarrow \frac{35x+28x+20x}{140}=1162$
$\Rightarrow 83x=1162\times 140\Rightarrow x=\frac{1162\times 140}{83}=1960$
$\therefore$ First part $=\frac{1960}{4}=490$
Second part $=\frac{1960}{5}=392$
Third part $=\frac{1960}{7}=280$.