A husband and wife, started painting their house, but husband left pai

A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?
A. 40/7
B. 50/7
C. 75/7
D. 55/7

As pointed out above there are several ways to solve this problem. Below are probably two shortest approaches:

Approach #1:

Rate of husband \(\frac{1}{20}\) job/day;
Rate of wife \(\frac{1}{15}\) job/day;
Combined rate: \(\frac{1}{20}+\frac{1}{15}=\frac{7}{60}\) job/day;

During the last 5 days, when the wife worked alone, she completed \(\frac{5}{15}=\frac{1}{3}\)rd of the job;
Hence, remaining \(\frac{2}{3}\)rd of the job was done by them working together in \(time=\frac{job'}{rate}=\frac{(\frac{2}{3})}{(\frac{7}{60})}=\frac{40}{7}\) days;

Total time needed to complete the whole job: \(5+\frac{40}{7}=\frac{75}{7}\) days.

Answer: C.


Approach #2:

It's based on observing the answer choices. On the PS section always look at the answer choices before you start to solve a problem. They might often give you a clue on how to approach the question.

Combined rate of the husband and wife is \(\frac{7}{60}\) job/day, which means that working together they'll complete the job in \(\frac{60}{7}\) days (time is reciprocal of rate). As they worked together only some part of the total time, then actual time would be more than \(\frac{60}{7}\) days. Only \(\frac{75}{7}\) is more than this value (answer choice C), so it must be correct.

Answer: C.

Hope it helps.