Question

A certain job was assigned to a group of men to do in 20 days. But 12 men did not turn up for the job and the remaining men did the job in 32 days. The original number of men in the group was:

• A. $31$
• B. $30$
• C. $32$
• D. $35$

Answer 1

Answer: (C)

$32$

Let the original no. of men in the group be $x$

According to the question-

$x$ men completes the job in $20$ days.

$(x-12)$ men completes the job in $32$ days.

$\therefore$ work done by $x$ men in $20$ days $=$ work done by $(x-12)$ men in $32$ days

$\Rightarrow x\times 20=(x-12)\times 32$

$\Rightarrow 20x=32x-384$

$\Rightarrow 12x=384$

$\Rightarrow x=32$

Hence, the original number of men in the group was $32$.