Question

$184$ is divided into two parts such that one-third of one part may exceed one-seventh of the other part by $8$, then the greater part is __________.

• A. $72$
• B. $110$
• C. $112$
• D. $114$

Answer 1

The correct option is C $112$

$x+y=184$.......(1)

$\frac{1}{3}x-\frac{1}{7}y=8$

Simplifying above equation we get

=$7x-3y=168$

$\therefore$ $x=\frac{168+3y}{7}$

Puttting these value of $x$ in equation (1) we get,

$\frac{168+3y}{7}+y=184$

Therefore $y=112$

Substituting value of $x$ in equation (1)

we get $x=72$

Hence the greater number = $112$