Aptitude - Time and Work - Discussion

^^ We do 20*16 & 16*15 because of the below logic:

It's given that 20W can do the work in 16 days. Going by this, 1W would be able to do the work in 16*20 days. Similarly, for one man, the work can be completed in 15*16 days. But then to find the capacity, you have to take the inverse, it's just like speed & time relation (the ratio of speed & time are reverse).

Hence, we write it as,
M:W = 1/240 : 1/320 = 1/3:1/4 = 4:3

@Dinesh: I feel if the fraction form is given a one of the answers then even that can be marked as the correct answer. But it's common practice to convert any answer into the simplest form & a fraction's not that.

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.

Though here there is no error but there is a shortcut:

The method is as follows

20w -> 16d
16m -> 15d

w:m=20:16=4:5 i.e., according to number of w and m
w:m=16:15 i.e., according to num of days they take

Then the ratio between m amd w according to their capacity will be
= (16:15 :: 4:5)
= 16/4 : 15/3
= 4:3

This could be done because the ratio of capacity is always reverse of number of days taken.

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.

As per the explation above, we can do the same thing by differnt manner.

It is confirmed from the question that work doen by women & men is same.

So we can write it in this way:

WORK OF WOMEN = WORK OF MEN

SO 20 WOMEN * 16 DAY = 16 MEN * 15 DAYS

SO 20*16/16*15 = MEN/WOMEN

SO RATIO IS 4:3.

Work done by the women

20 women -->16 day
1 women ----16/20
One day work of 1 women 20/16

Work done by a man
16 man ---->15
1 man ------>15/16
one day work of 1 man 16/15

(1-day work of one man) : (1-day work of one woman)

(20/16) / (15/16)
20/15 = 4/3 i.e 4:3.

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.

We can easily find out the answer for this question by reverse thinking.

Take an option A.
Divide 16 by 3 it can't. We can't Divide it exactly. So it is not an answer.

Take option B.
Divide 16 by 4 and 15 by 3 hence it is the answer.

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.

Take it very simple.

Apply the basic rule of ratio:

A:B=1/240:1/320.

Now (1/240)/(1/320).

By solving:
(1/240)*(320/1)
=320/240
=4/3 i.e. 4:3.