GATE Overflow Test Series | Quantitative Aptitude | Test 1 | Question: 30

Question

A contractor undertakes to complete a work in $155$ days. He employs $300$ men for $50$ days and they complete half of the work . He then reduces the number of men to $200,$ who work for $40$ days, after which there are $15$ days holidays. How many men must be employed for the remaining period to finish the work?

• A. $140$
• B. $60$
• C. $150$
• D. $200$

Answer 1

Work done by $300$ men for $50$ days $ = 300M \times 50D = 15000MD$
 
 Lets say total work is $'W'\,\,\text{unit}.$
 
 $\implies \dfrac{1}{2} W = 15000 MD$
 
 $\implies W = 30000 MD$
 
 Remaining work $ = 30000MD - 15000MD = 15000 MD$
 
 Work done by $200$ men for $40$ days $ = 200M \times 40D = 8000 MD$
 
Remaining work $ = 15000 MD - 8000MD = 7000 MD$

Remaining time $ = 155 - (50 + 40 + 15) = 155 - 105 = 50$ days

Lets say remaining work is done by $'x'$ men in $50$ days.

$\implies x M \times 50D = 7000 MD$

$\implies x = 140$ men is needed.

So, the correct answer is $(A).$