Question: A is thrice as efficient as B and hence takes 12 days less to complete a work as compared to B. Find the number of days in which they can complete the work while working together?

1. 3
2. 4.5
3. 6
4. 6.5
5. 7.5

Correct Answer: B

Solution and Explanation:

Approach Solution 1:
Set the rates as A and B. A = 3B, it takes A: 1/A= 1/3B days to complete the job and B: 1/B days to complete the job.

The difference is 12 days, so 1/B−1/3B= 2/3B= 12.

B = 2/(3*12) = 1/18, A = 3*B = 1/6.

Finally, their combined rate is A + B = 1/6 + 1/18 = 4/18 = 2/9, it will take 9/2 days to complete the job.

Approach Solution 2:
Let efficiency of B be e ; efficiency of a will be 3e

So,

de=(d−12)3e
de=(d−12)3e

Or,

d=(d−12)3
d=(d−12)3

Or,

d=3d−36
d=3d−36
So, 2d = 36
hence, d = 18

Thus, time taken by both of them will be 18*1/3+1 = 4.5 days

“A is thrice as efficient as B and hence takes 12 days less to complete”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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