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 many days will they take to complete the remaining work ?

• A. $3$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (C)

$6$

$12$ children take $16$ days to complete a work

$8$ adults take $12$ days to complete the same job.

Let the productivity of children be $c$ and the productivity of adult be $m$

Thus,

$12c\times 16=8m\times 12$

$=>c=\frac{1}{2}m$

Work done by $8$ men in $12$ days $8m\times 12$ $=96m$

Work done by $16$ men in $3$ days $=16m\times 3$$=48m$

Work left $=96m-48m=48m$

After $3$ days $10$ adults left and $4$ children joined them

Thus, $6$ men and $4$ children have to complete the remaining job.

Let the time taken by them be $t$ days.

Thus

$(6m+4c)t=48m$

$=>t=\frac{48m}{6m+4\times \frac{1}{2}m}$

$=>t=\frac{48m}{6m+2m}$

$=>t=6$