Question

2. The work done by a woman
in 8 hours is equal to the work done by a man in 6 hours and the work done
by a boy in 12 hours. If working 6 hours per day, 9 men can complete a won
18 o nours per day, 9 men can complete a work in 6 days, then in how
many days can 12 men, 12 women and 12 boys together finish the same work working 8 hours per day?​

Answer 1

Ratio of time taken by a woman, a man and a boy

=8:6:12=4:3:6

So, 4 women ≡ 3 men ≡ 6 boy

(12 mens + 12 womens + 12 boys)

=[12+(34×12)+(36×12)]men = (12+9+6)men=27 men

Let the required number of days be x

More men, Less days (Indirect proportion)

More working hours, Less days (Indirect proportion)

Working hours 8:6Men 27:9}::6:x

∴27×8×x=9×6×6⇔x=(9×6×6)(27×8)⇔x=32⇔x=112