Two Consultants, Mary and Jim, Can Type up a Report in 12.5 Hours and Edit it in 7.5 Hours.

Question: Two consultants, Mary and Jim, can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, approximately how many hours will it take if Jim types the report and Mary edits it immediately after he is done?

1. 41.4
2. 34.1
3. 13.4
4. 12.4
5. 10.8

“ Two consultants, Mary and Jim, can type up a report in 12.5 hours and edit it in 7.5 hours.” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT by Mathivanan Palraj". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach 1

Let us consider that Jim has to type the report in x hours.
Let us consider that Mary types the report in y hours.
So, the equation becomes:
1/x + 1/y = 1/12.5
implies, 1/x + 1/30 = 1/12.5
implies, (30 + x)/30x = 1/12.5
implies, 375 + 12.5x = 30x
implies, 375 = 17.5x
implies, x = 150/7

Let us consider that Jim edits the report in a hour and let Mary edit the report in b hours.
Then the equation becomes:
1/a + 1/b = 1/7.5
implies, 1/12 + 1/b = 1/7.5
implies, b + 12 = 12b/7.5
implies, 7.5b + 90 = 12b
implies, 90 = 4.5b
implies, b = 20

Therefore, the time is taken Jim to type the report and for Mary to edit it = 150/7 + 20 = 41.4
Hence, the correct answer is option A.

Approach 2

Let us break the break the time to type and edit in two parts:
Mary needs 30 hours to type the report,
So, Mary's typing rate =1/30 job/hour;
Mary and Jim can type up a report together in 12.5 hours.
So, 1/30 + 1/x = 1/12.5
This equals 2/25, where x is the time needed for Jim to type the report.
Solving this equation, we get:
x=150/7

Again, Jim needs 12 hours to edit the report. So, Jim's editing rate = 1/12 job/hour;

Therefore, Mary and Jim can edit a report in 7.5 = 1/y + 1/12 = 1/7.5
(here y is the time needed for Mary to edit the report alone)
Solving this equation, we get:
y=20
Time is taken by Jim if he types the report and Mary edits it immediately after he is done x+y= 150/ 7 +20 ≈ 41.4

Correct Answer: A

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