A man, a woman, and a boy individually can complete a certain work in 6, 8, and 24 days respectively. How many boys must assist one man and two women such that the work is completed in 2 days?
Answers
Given :
A man , a woman and a boy can complete a certain work in 6 , 8 and 24 days respectively.
To Find :
How many boys must assist one man and two women such that the work is completed in 2 days
Solution :
A man and 2 women and a boy complete work in 1 day = 1/6 + 2×1/8 + 1/24 = 11/24 of work
A man and 2 women and a boy complete work in 2 days = 2 × 11/24 = 11/12 of work .... (1)
Now
A man and 2 women complete work in a day =
1/6 + 2×1/8 = 10/24 of work
A man and 2 women complete work in 2 days =
2 × 10/24 = 10/12 of work .... (2)
Total remaining work for some number of boys =
1 - 10/12 = 2/12 of work
Therefore 2/12 of the work is to be finished by boys only so that the work complete in 2days only
Now subtracting equation 2 from equation 1 we get :
A boy complete work in 2days = 11/12 - 10/12 = 1/12 of work
So remaining work is completed by number of boys , so that work can complete in 2days only =
= 2 boys
Thus 2 boys must assist one man and two women such that the work is completed in 2 days.
Given :
A man , a woman and a boy can complete a certain work in 6 , 8 and 24 days respectively.
To Find :
How many boys must assist one man and two women such that the work is completed in 2 days
Solution :
A man and 2 women and a boy complete work in 1 day = 1/6 + 2×1/8 + 1/24 = 11/24 of work
A man and 2 women and a boy complete work in 2 days = 2 × 11/24 = 11/12 of work .... (1)