Question

A group of $25$ teachers, $20$ engineers, $18$ doctors and $12$ salesmen visited a fair and spent Rs $13,300$ altogether. It was found that 5 teachers spent as much as $4$ engineers, $12$ engineers spent as much as $9$ doctors and $6$ doctors spent as much as $8$ salesmen. If every person in a group spent the same amount, find the amount spent by each engineer.

• A. Rs $140$
• B. Rs $175$
• C. Rs $180$
• D. Rs $210$

Answer 1

The correct option is B Rs $175$

Let the amount spent by a teacher, Engineer, Doctor and Salesman be Rs x, Rs y, Rs z and Rs w respectively.
$⟹5x=4y$; $12y=9z$ and $6z=8w$
$⟹15x=12y=9z=12w=k$ (say)
$\therefore x=\frac{k}{15}$, $y=\frac{k}{12}$, $z=\frac{k}{9}$, $w=\frac{k}{12}$
we have total spending $=Rs13,300$
$\therefore 25\times \frac{k}{15}+20\times \frac{k}{12}+18\times \frac{k}{9}+12\times \frac{k}{12}=13300$
$⟹k=2100$
$\therefore y=\frac{k}{12}=\frac{2100}{12}=175$