Question

$12$ children take $16$ days to complete a work which can be complete by $8$ adults in $12$ days. $16$ adults started working and after $3$ days $10$ adults left and $4$ children joined them . How many days will it take them to complete the remaining work ?

• A.
  $6$
• B. $8$
• C. $4$
• D. $3$

Answer 1

The correct option is A

$6$

Let the complete work $=x$.

12 children can do x work in 16 days.

So 1 child will do x work in $12\times 16$ days $=192$ days.

$\therefore$ In 1 day 1 child will do $\frac{x}{192}$ work.

Similarly, 8 adults can do x work in 12 days.

So 1 adult will do x work in $8\times 12$ days $=96$ days.

$\therefore$ In 1 day 1 adult will do $\frac{x}{96}$ work.

$\therefore$ 16 adults in 3 days do $\frac{3\times 16\times x}{96}$ work

=$\frac{x}{2}$ work.

Rest of the work=x=$\frac{x}{2}$ work=$\frac{x}{2}$ work.

This work is done by $(16-10)$ adults $=6$ adults and 4 children.

In 1 day 6 adults will do $\frac{6x}{96}$ work=$\frac{x}{16}$ work &

in 1 day 4 children will do $\frac{4x}{192}$ work=$\frac{x}{48}$ work.

So, in 1 day 6 adults + 4 children will do

$(\frac{x}{16}+\frac{x}{48})$ work=$\frac{x}{12}$ work.

So $\frac{x}{2}$ work will be completed in

$\frac{x}{2}÷\frac{x}{12}$ days $=6$ days.

Then the rest of the work will be completed in 6 days.

Ans- Option A.