Nine boys can complete a work in 360 days, 18 men can complete the same work in 72 days and 12 women can complete it in 162 days. In how many days, can 4 men, 12 women and 10 boys together, complete the work?
Answer & explanation
Correct answer: option 2
ATQ, for doing the work, required persons:
In 360 days ⇒ 9 boys
In 01 day = (360 × 9) boys .........(i)
In 72 days ⇒ 18 men
In 01 day = (72 × 18) men .........(ii)
In 162 days ⇒ 12 women
In 01 day = (162 × 12) women .........(iii)
From eq. (i), (ii) & (iii), we get,
⇒ (360 × 9) boys = (72 × 18) men = (162 × 12) women
⇒ 5 boys = 2 men = 3 women .............(iv)
Now,
We have a group of (10 boys + 12 women + 4 men) ................(v)
From eq. (iv)
⇒ 5 boys = 2 men ⇒ 10 boys = 4 men.
⇒ 3 women = 2 men ⇒ 12 women = 8 men.
Now, convert no. of boys and women into no. of men in eq. (v)
We have, 4men + 8 men + 4 men = 16 men to finish the work now.
ATQ,
18 men can do the work in: 72 days,
01 men can do the work in: (72 × 18) days.
16 men can do the work in: \(\frac{72×18}{16}\)= 81 days