Question

4 man 6boys can finish a work in 5days while 3man 4boys can finish in 7days.Find the time taken by 1men or alone by 1 boy?

Answer 1

Answer:

Let be the number of days by man = x

and number of days by boy = y

and

work done by day of 1 man = 1/x

work done by day of 1 boy = 1/y

According to Question

5(4/x+6/y) = 1

4/x+6/y = 1/5 ......(i)

and

7(3/x+4/y) = 1

3/x+4/y = 1/7 ........(ii)

puting the 1/x = q , 1/y = p

4q+6p = 1/5

20q+30p = 1 .........(i)

and,

3q+4p = 1/7

21q+28p = 1 ..........(ii)

by (i) and (ii)

20q+30p = 1 × 21 .......(i)

21q+28p = 1 × 20 ........(ii)

Multipaction by 21 in (i) and by 20 in (ii).

420q+630p = 21

420q+560p = 20

- - -

______________

70p = 1

p = 1/70

by (i)

20q+30p = 1

20q+30×1/70 = 1

140q+30/70 = 1

140q+30 = 70

140q = 70-30

140q = 40

q = 40/140

q = 2/7

1/x = q | 1/y = p

1/x = 2/7 | 1/y = 1/70

x = 7/2 | y = 70

work done by day of 1 man = 3.5 days

work done by day of 1 boy = 70 days.

please mark me Brianlist