Question

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

(a) 6

(b) 8

(c) 4

(d) 3

Answer 1

Correct option is (a) 6

12 children take 16 days to complete a work.

So, 1 child's 1 days' work = \(\frac 1{12 \times 16} = \frac 1{192}\) 

8 adults take 12 days to complete a work.

So, 1 adult's days' work = \(\frac 1{8 \times 12} = \frac 1{96}\)

16 adults' 3 days' work = \(16 \times 3 \times \frac 1{96} = \frac 12\)

Remaining work = \(1 - \frac 12 = \frac 12\)

Now (6 adults' + 4 children's) 1 days' work = \(\frac 6 {96} + \frac 4{192}\)

\(= \frac{16}{192} \)

\(= \frac 1{12}\)

∴ \(\frac 1{12}\)​th of the work is done by them in 1 day

∴ \(\frac 1{12}\) of the work will be done in \(\frac 1{1/12} \times \frac 12\) days = 6 days