TANCET - XAT Math Problem : Ratio Proportion

Question

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

1. 8 men
2. 2 men
3. 122 men
4. 24 men

Choice (3). Correct Answer - 122 men.

Explanatory Answer

Amount of work done by 20 men = 24 women = 40 boys or amount of work done by 1 man = 1.2 women = 2 boys.

Let us therefore, find out the amount of men required, if only men were working on the task, to complete the new job under the new conditions.

And then make adjustments for the women and boys who are already employed on the task.

The man hours required to complete the new task = 4 times the man hours required to complete the old task. (As the new task is 4 times as big as the old task)

So, the new task is 20 * 12 * 8 * 4 men hours task.

Let 'n' be the number of men required to complete the new task.
Equating the men hours of task, we get 20 * 12 * 8 * 4 = n * 5 * 12. Or n = 128.

The new task will require 128 men, if only men worked on the task to complete it.

However, the problem states that 6 women and 2 boys are working on the job.

6 women are the equivalent of = 5 men and 2 boys = 1 man.

i.e., the equivalent of 5 + 1 = 6 men are already working on the project.

Therefore, 122 more men are required to work with 6 women and 2 boys to complete the task.