Ratio and Proportions - Quant/Math - CAT 2009
Question 4 the day:
June 7, 2002
The question for the day is from the topi Ratio and Proportions.
- 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 take to do a job four times as big working for 5 hours a day for 12 days?
| (1) | 8 men | | (2) | 12 men | | (3) | 2 men | | (4) | 24 men |
Correct Answer - (3)
Solution:
Amount of work done by 20 men = 24 men = 40 boys or 1 man = 1.2 woman = 2 boys.
Let us therefore, find out the amount of men required, if only men were working on the job, to complete the new job under the new conditions and then make adjustments for the women and children working with the men.
The man hours required to complete the new job = 4 times the man hours required to complete the old job. (As the new job is 4 times as big as the old job)
Let ‘n’ be the number of men required.
20 * 12 * 8 = n * 5 * 12 * 4. n = 8.
8 men working will be able to complete the given job.
However, the problem states that 6 women and 2 boys are working on the job.
6 women =  = 5 men and 2 boys = 1 man. The equivalent of 5 + 1 = 6 men are already working.
Therefore, 2 men a required to work with 6 women and 2 boys to complete the job.
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