Aptitude - Time and Work - Discussion

Its very simple,

WOMEN = 20 * 16 = 240.
MEN = 16 *15 = 320.
MEN/WOMEN =320/240 =4/3 (used 80's table).
RATIO = 4 : 3..

Hope this helps.
Thanks.

(20w) 16:(16m) 15.
By Cancellation: We get 4:3.

20 women ---> 16 days.
20 women ---> 1/16 work in one day.
1 woman ---> 1/ (16*20) in one day.

In the same way,
16 men---> 15 days.
16 men---> 1/15 work in one day.
1 man---> 1/ (15*16) in one day.

To calculate the ratio,
1/ (15*16) : 1/(16*20).
By cancelling 16 on both sides and cancelling 15 and 20 as 3 and 4.

1/3:1/4.
Cross multiply we get;
4:3.

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.

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

Women = 20 * 16 = 240,
Men = 16 * 15 = 320,
Men/women=320/240 = 4/3.
Ratio = 4:3.

M1 * D1 = M2 * D2.
20*16 = 16*15,
4 = 3,
4:3.

Why Cross multiplied in the last step? Please explain.

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.

It should be option A.

Men:women=240:320.
=3:4.
Here, the question is asking the ratio for men and women, but not for women and men.