Aptitude - Time and Work - Discussion

3:4 is the correct use formula M1D1/W1 = M2D2/W2.

Here is a simple solution.

20 women do it in 16 days,
16 men do the same in 15 days,
So as the work is the same 20X16 : 16X15,
or that comes to 20:15 as the 16 is common in both the sides.
20:15 ratio is 4:3. done.

30 women can do a work in 15 days. 15 men can complete the same work in 20 days. What is the ratio between the capacity of a man and a woman?

Can Anyone solve this?

@Karthick.

The Answer is 3:2.

Formula: M1 H1 D1 = M2 H2 D2.
M (men, women, children).

So 20women * 16 days = 16 men * 15days,
20*16=16*15,
320 = 240 ( we get ),
4 = 3 ( after simplified).
So, 4:3.

It should be option A.
Men:women = 240:320.
=3:4.
The question is asking the ratio for men and women, but not for women and men.

1 man can complete work in 320 days.
Whereas 1 woman can complete work in 280 days.

So work done by 1 man in 1 day is 1÷320.
Work done by 1 woman in 1 day is 1÷240.

1÷320:1÷240 = 240:320 = 3:4.

We can conclude this by saying women have more ability to do work.

Why Cross multiplied in the last step? Please explain.

Why is it not 3:4 as m:w is 16*15/16*20? Please explain this.

Work done by one woman in a day = Total work/(Number of women * Number of days).
= 1/(20 * 16).

Work done by one man in a day = Total work/(Number of men * Number of days).
= 1/(16 * 15).

The ratio of man's capacity to woman's capacity = (1/(16 * 15))/(1/(20 * 16)).

Simplifying the expression, we get:

The ratio of man's capacity to woman's capacity = (20 * 16)/(16 * 15).
= 20/15,
= 4/3.

Therefore, the ratio between the capacity of a man and a woman is 4:3.