Question: 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?

1. 40/7
2. 50/7
3. 75/7
4. 55/7

Correct Answer: C
Solution and Explanation:
Approach Solution 1:

The problem statement discloses that:

Given:

• A husband and wife started painting their house.
• The husband left painting 5 days before the completion of the work.
• The husband alone would have completed it in 20 days and wife in 15 days.

Find out:

• The days required to complete the work.

The rate of the husband = 1/20 job/day;
The rate of the wife = 1/15 job/day;
Therefore, the combined rate = 1/20 + 1/15 = 7/60 job/day;

When the wife worked alone in the last 5 days, she completed = 5/15 =⅓ rd of the job;
Hence, the time required by husband and wife to do the remaining ⅔ rd of the job by working together = job′/rate = (2/3)/(7/60) = 40/7 days;
Total time required to complete the entire job: 5 + 40/7 = 75/7 days.

Approach Solution 2:

The problem statement informs that:

Given:

• A husband and wife started painting their house.
• The husband left painting 5 days before the completion of the work.
• The husband alone would have completed it in 20 days and wife in 15 days.

Find out:

• The days required to complete the work.

Let’s solve the question by analysing the answer options.
Since husband alone takes 20 days and wife takes 15 days to finish the work, then the combined rate of the husband and wife = 1/20 + 1/15= 7/60 job/day.
This indicates that working together they'll finish the job in 60/7 days (time is reciprocal of rate).

Since they worked together for only some part of the total time, the exact time would be more than 60/7 days.
Therefore, by analyzing the answer choices we find only 75/7 is more than this value.
Hence, the total time required to complete the entire job = 75/7 days.

Approach Solution 3:

The problem statement informs that:

Given:

• A husband and wife started painting their house.
• The husband left painting 5 days before the completion of the work.
• The husband alone would have completed it in 20 days and wife in 15 days.

Find out:

• The days required to complete the work.

Let the total time required to complete the work be x.
The husband left painting 5 days before the completion of the work and alone he takes 20 days to finish the entire work.
Therefore, the work time of the husband = (x-5)/20
The wife takes 15 days alone to finish the entire work
Therefore, the work time of the wife = x/15

Hence, the total work time for husband and wife, when working together = (x-5)/20 + x/15
(x-5)/20 + x/15 = 1
By simplifying, we get:
=> (3x-15)/60 + 4x/60= 1
=> 7x-15=60
=> 7x=75
=> x=75/7

Therefore, the total time required to complete the work is 75/7 days.

“A husband and wife, started painting their house, but husband left”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “501 GMAT Questions”. GMAT Problem Solving questions help the candidates to consider facts given in the question to solve numerical problems. GMAT Quant practice papers enable the candidate to become acquainted with lots of questions that will boost their confidence to score better in the exam.

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