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?

81

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