Question

M does ${\frac{5}{6}}^{th}$ of the work in 25 days. He then calls in N and they together finish the remaining work in 4 days. How long would N alone take to do the whole work?

• A. 80 days
• B. 150 days
• C. 120 days
• D. 100 days
• E. None of these

Answer 1

The correct option is C

120 days

Whole work is done by M in $(25\times \frac{6}{5})=30days$

Now, $(1-\frac{5}{6})$ i.e., $\frac{1}{6}$ work is done by M and N in $4days$

Whole work will be done by M and N in $(4\times 6)=24days$

M's 1 day's work = $\frac{1}{30}$, (M+N)'s 1 day's work = $\frac{1}{24}$

N's 1 day's work = $(\frac{1}{24}-\frac{1}{30})=\frac{1}{120}$

So, N alone would do the work in 120 days.