20 men and 24 women started working together They worked together for 0 6D days After that B number ...........

Quantitative Aptitude(IBPS PO) Time and work

Directions: Answer the question based on the information given below: X men can complete a work in Y days. Y women can complete the work in X days. 20 men and 16 women working together can complete the same work in 53 1/3 days.

20 men and 24 women started working together. They worked together for 0.6D days. After that B number of boys did the work in 0.45D days, then the whole work is completed which B number of boys can complete it in D days. What is the value of D?

This questions was previously asked in

IBPS PO Mains (26th November 2022)

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Explanation:

Correct option is 2:40

X men can complete the work in Y days,
So,
1 man can complete the whole work in XY days.
Y women can complete the work in X days.
So,
1 woman can complete the whole work in XY days.
It is given that 20 men and 16 women can complete the work in 53 1/3 days = 160/3 days.
So,
20/XY + 16/XY = 3/160
36/XY = 3/160
XY = 1920.
So the total work is 1920.
20 men and 24 women started working together and they worked together for 0.60 days,
So the work completed in 0.6D days is (20+24) x 0.6D = 26.4D.
After that B number of boys did the work in 0.450 days,
So, the work done is 8 x 0.45D = 0.45BD.
So the total work done is = 26.4D+ 0.45BD... (1)
The whole work is completed which B number of boys can complete it in D days,
BD = 1920
Put this in equation (1),
So the total work done is 26.4D+ 0.45 x 1920= 26.4D+ 864
But the total work that is done is 1920,
So,
1920 = 26.4D + 864
D= 10560/264 = 40 days.
So the value of D is 40.