Question

15 men can complete a work in 210 days. They started the work but at the end of 10 days 15 additional men, with double efficiency, were inducted. How many days, in whole, did they take to finish the work?

• A. \(72\frac{1}{2}\) days
• B. \(84\frac{3}{4}\) days
• C. \(76\frac{2}{3}\) days
• D. 70 days

Answer 1

The Correct Option is C

Total man days = \(210 \times 15 = 3150\)
Man days:
for 1st 10 days = \(10 \times 15 = 150\)
Let now days taken be \(d\) after induction of 15 men. {double efficency means 1 men can be counted twice, so 30 men}
Total men now = \(15 + 15\times2 = 45\) men
\(\Rightarrow\;\)\(45d + 150 = 3150\) 
d = \(\frac{200}{3}\)
Total days = \(\frac{200}{3} + 10 = \frac{230}{3}\) = \(76\frac{3}{2}\) days