Question

X can do a piece of work in 12 days which Y can do in 18 days. They begin together but 6 days before the completion of the work, X leaves. The total number of days to complete the work is?

• A. 33/5 days
• B. 17/2 days
• C. 54/5 days
• D. 27/2 days
• E. None of these

Answer 1

The correct option is C

54/5 days

Y's 6day's work = $(\frac{1}{18}\times 6)=\frac{1}{3}$, Remaining work = $(1-\frac{1}{3})=\frac{2}{3}$

(X + Y)'s 1day's work = $(\frac{1}{12}+\frac{1}{18})=\frac{5}{36}$

Now, $\frac{5}{36}$ work is done by X and Y in 1 day

$\therefore$ $\frac{2}{3}$ work is done by X and Y in $(\frac{36}{5}\times \frac{2}{3})=\frac{24}{5}days$

Hence, total time taken = $(6+\frac{24}{5})days$ = $10\frac{4}{5}days$.