Question

if 12 men and 16 boys can do a work in 5 days and 13 men and 24 boys can do the same work in 4 days find how long will the 7 men and 10 boys will take to do it​

Answer 1

Step-by-step explanation:

5(12 M + 16 B) = 4(13 M + 24 B)

60M + 80B = 52M + 96B

That gives, 8M = 16B, which is , 1M=2B

Now, 12 M + 16B can do work in 5 days.

So, 12 M + 8 M can do work in 5 days.

So, 20M can do work in 5 days.

Now, 7M + 10B = 7M + 5M = 12 M

Hence, if 20M can do work in 5 days, 12M can do work in (20*5)/12 = 8.33 days.

Answer 2

12 men + 16 boys can do a piece of work in = 5 days

60 men + 80 boys can do a piece of work in = 1 day . . . . . . . . . (i)

and 13 men + 24 boys can do the same work in = 4 days

52 men + 96 boys can do the same work in = 1 day . . . . . . (ii)

From (i) and (ii)

60 men + 80 boys = 52 men + 96 boys

⇒ 60 men – 52 men = 96 boys – 80 boys

⇒ 8 men = 16 boys

$\sf{1 man = \frac{16}{8} = boys}$

12 men + 16 boys = 12 x 2 + 16 = 24+16 = 40 boys

Now, in first case,

In the second case,

7 men + 10 boys = 7 x 2 + 10 = 14 + 10 = 24 boys

Now 40 boys can do a piece of work in = 5 days

1 boy can do the same work in = 5 x 40 days

and 24 boys will do the same work in

$= \sf{ \frac{5 \times 40}{24} \: days}$

$= \sf{ \frac{25}{3} }$

$= \sf{8\frac{1}{3} \: days}$