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

Hint: It is given that 210 men finish the work in 60 days. So, the fraction of work done by 1 man in a day is \[\dfrac{1}{210\times 60}\]. Now, use the unitary method and calculate the fraction of work done by 210 men in 12 days. Then, calculate the remaining fraction of the work to be done. After 12 days, 70 more men joined. Calculate the total number of men who are working after 12 days. Assume that it took x days to complete the remaining work. Now, using the unitary method, calculate the fraction of work done by 280 men in x days. The fraction of work done in x days is equal to the fraction remaining work. Solve it further and calculate the value of x.

Complete step-by-step solution
According to the question, it is given that the contractor employed 210 men to build a house in 60 days. After 12 days, he was joined by 70 more men.
The time required by 210 men to finish the work = 60 days
Fraction of work done by 1 man in a day = \[\dfrac{1}{210\times 60}\] ……………………………….(1)
Now, using the unitary method,
The fraction of work done by 210 men in 12 days = \[\dfrac{210\times 12}{210\times 60}=\dfrac{12}{60}=\dfrac{1}{5}\] ……………………………………(2)
After 12 days, the fraction of remaining work = \[1-\dfrac{1}{5}=\dfrac{4}{5}\] ………………………………………….(3)
After 12 days, it is given that 70 more men joined.
The total number of men = \[210+70\] men = 280 men ………………………………………(4)
Let us assume that it took x days to complete the remaining work.
Using equation (1) and unitary method, we get
The fraction of work done in x days = \[\dfrac{280\times x}{210\times 60}=\dfrac{4x}{180}=\dfrac{x}{45}\] …………………………………..(5)
Clearly, We can say that the fraction of work done in x days is equal to the fraction remaining work.
Now, from equation (3) and equation (5), we get
\[\begin{align}
  & \Rightarrow \dfrac{4}{5}=\dfrac{x}{45} \\
 & \Rightarrow \dfrac{4}{5}\times 45=x \\
\end{align}\]
\[\Rightarrow 36=x\] …………………………………..(6)
Therefore, it took 36 days to complete the remaining work.
Hence, the correct option is (B).

Note: In this question, one might make a silly mistake and calculate the fraction of work done by 1 man in a day equal to \[\dfrac{60}{210}\]. This is wrong. The fraction of work done by 1 man in a day must be equal to
\[\dfrac{1}{210\times 60}\] . Therefore, be careful while calculating the work done by 1 man in a day using a unitary method.