Question

20. i 10 men. 8 women and 6 boys can complete a piece of work in 25 days, for how
many days will 19 men, 20 women and 30 boys be occupied upon three times the
work. If the work of 6 men be equal to the work of 10 women or equal to the work of 15 boys​

Answer 1

Answer:

30 days will be needed to complete three times the work.

Answer 2

10 men. 8 women and 6 boys can complete a piece of work in 25 days, if the work of 6 men be equal to the work of 10 women or equal to the work of 15 boys.

We have to find the no of days taken to compete the three time of the same work by 19 men, 20 women and 30 boys.

∵ work of 6 men = work of 10 women = work of 15 boys

∴ the ratio of efficiencies of man, woman and boys = 1/6 : 1/10 : 1/15 = 5 : 3 : 2

Now total units of work done by 10 men , 8 women and 6 boys in 25 days

⇒total units of work = (10men + 8 women + 6boys) × 25 days

= (10 × 5 + 8 × 3 + 6 × 2) × 25 units

= (50 + 24 + 12) × 25

= 86 × 25 units

Let three times of the work is done by (19 men + 20women + 30 boys) in x days.

⇒3 × (86 × 25) units = (19 men + 20 women + 30 boys) × x days

⇒3 × (86 × 25) = (19 × 5 + 20 × 3 + 30 × 2) × x

⇒3 × 86 × 25 = (95 + 60 + 60) × x

⇒x = (3 × 86 × 25)/215 = 30 days

Therefore the number of days taken by them is 30 days