Question

A contractor employed $210$ men to build a house in $60$ days. After $12$ days, he was joined by $70$ more men. In how many days will the remaining work be finished?

• A. $35$days
• B. $36$days
• C. $38$days
• D. $40$days

Answer 1

The correct option is B $36$days

Given that,

Let the total work to be done $=1$

$210$ men build a house in $60$ days

each man $1$ day work $=\frac{1}{210\times 60}$

After $12$ days,

Total work done by $210$ workers in $12$ days

$=\frac{1}{210\times 60}\times 210\times 12$$=\frac{1}{5}$

$70$ extra workers joined the work now

total workers $=280$

Remaining work $=1-\frac{1}{5}=\frac{4}{5}$ .............(1)

Let the remaining work finished in next $X$ days

Total work done by $280$ workers in $X$ days $=\frac{1}{210\times 60}\times 280\times X$ ..................(2)

Equation $\left(1\right)=\left(2\right)$

$\frac{4}{5}=\frac{1}{210\times 60}\times 280\times X$

$X=36$ Days