Question

4 men and 6 boys can finish a piece of work in 5 days while 3 men and 4 women can finish it in 7 days. Find the time taken by 1 man alone or that by 1 boy alone.
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PLEASE HELP ME.

Answer 1

Let 1 men's work = x.

Let 1 boy's work = y.

Given that 4 men and 6 boys can finish a work in 5 days.

= > 4x + 6y = 1/5  ----- (1) 


Given that 3 men and 4 women can finish a work in 7 days.

= > 3x + 4y = 1/7  ----- (2)


On solving (1) * 3 & (2) * 4, we get

12x + 18y = 3/5

12x + 16y = 4/7

--------------------------

          2y = 1/35

            y = 1/70



Substitute y = 1/70 in (1), we get

= > 4x + 6y = 1/5

= > 4x + 6(1/70) = 1/5

= > 4x + (6/70) = 1/5

= > 4x = 1/5 - 6/70

= > 4x = 4/35

= > x = 4/140

= > x = 1/35


Therefore 1 man alone can complete it 35 days.

1 boy alone can complete in 70 days.


Hope this helps!