Question

S and T can complete a work in 30 days and 20 days respectively. They started doing the work together, but after 4 days, T had to leave and S alone completed the remaining work. The whole work was completed in:

• A. 16 days
• B. 20 days
• C. 24 days
• D. 30 days
• E. 38 days

Answer 1

The correct option is C

24 days

(S+T)’s 1 day’s work $=(\frac{1}{30}+\frac{1}{20})=\frac{1}{12}$

Work done by S and T in 4 days $=(\frac{1}{12}\times 4)=\frac{1}{3}$,

Remaining work $=(1-\frac{1}{3})=\frac{2}{3}$

Now, $\frac{1}{30}$ work is done by S in 1 day.

∴ $\frac{2}{3}$ work will be done by S in $(30\times \frac{2}{3})=20days$

Hence, total time taken $=(20+4)=24days$