GMAT Problem Solving- If 20 Men or 24 Women or 40 Boys can do a Job in 12 Days

Question: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?

1. 44
2. 50
3. 120
4. 122
5. 128

‘If 20 Men or 24 Women or 40 Boys can do a Job in 12 Days GMAT Problem Solving’ is the topic from the GMAT Quantitative problem set. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. 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 Solution 1:

As per the problem statement, it is given that 20 men work for 12 days for 8 hours to do a job.
So the number of men required to complete the work in 12 days working 5 hours is:
=> (20*8)/5 =32
Since12 days are constant for both the scenarios, let's keep it as a constant.
Since, 20 men take 8 hours to complete the job, the number of men required if work is done only for 1 hour a day
= 8*20 men(more men as hours worked are less)
No of men required if work is done for 5 hours a day
= (8*20)/5 (less men required now)

Since the work is 4 times as big as the previous one, so no of men required will be = 4*32 = 128
Now we already have 6 women and 2 boys. we need to convert them to men to find the remaining no of men required

24W=20M, or 6W=(20*6)/24 = 5 Men

40B=20M, or 2B = (20*2)/40 = 1 Men

So number of men required = 128-(5+1) = 122

Correct Answer: D

Approach Solution 2:

We can let the job = 1, and we are given that the job can be completed in 12 x 8 = 96 hours by 20 men or 24 women or 40 boys. Let’s determine the rate of 1 man per hour, which is (1/20)/96 = 1/(20 x 96). Similarly, the rate of 1 woman per hour is (1/24)/96 = 1/(24 x 96) and the rate of 1 boy per hour is (1/40)/96 = 1/(40 x 96).

Now we are given that another job is four times as big, and thus this new job = 4. We also are given that 6 women, 2 boys, and some number of men will be working on this job for 5 x 12 = 60 hours. We need to determine the number of men needed. We can let the number of men needed = n and create the following equation:

6 * 1/(24 x 96) * 60 + 2 * 1/(40 x 96) * 60 + n * 1/(20 x 96) * 60 = 4

360/(24 x 96) + 120/(40 x 96) + 60n/(20 x 96) = 4

Multiplying the entire equation by 96, we have:

360/24 + 120/40 + 60n/20 = 384

15 + 3 + 3n = 384

3n = 366

n = 122

Correct Answer: D

Approach Solution 3:

It is assumed in the problem statement that 20 workers will work a job for 12 days in a row for 8 hours each day.
Therefore, 20*8/5 = 32 workers are needed to finish the job in 12 days at a rate of 5 hours each day.
We'll continue to treat the 12 days as a constant as they are the same for both situations.
Since it takes 20 men 8 hours to finish the job, the needed number of men if labour is only done for 1 hour every day is 8*20 men (more men as hours worked are less)
If labour is done for 5 hours every day, the number of men needed is (8*20)/5. (less men required now)

Since the task is four times as large as the previous one, 128 workers will be needed, or 4 * 32
We currently have 6 females and 2 males. In order to determine the remaining number of men needed, we must turn them into men.

6W=(20*6)/24 = 5 Men, or 24W=20M

2B = (20*2)/40 = 1 Men, or 40B = 20M

Thus, the necessary number of men is 128-(5+1) = 122.

Correct Answer: D

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