Question

If 8 men and 6 boys can dig a well in 2 days and 6 men and 2 boys can do it in 3 days how long will 5 men and 3 boys take to do it

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Let consider:-

1 man can dig a well in = x days

1 boy can dig a well in = y days.

work done by a man in 1 day= $\frac{1}{x}$ days

work done by 1a boy in 1 day = $\frac{1}{y}$ days

Total work done by 8 men and 6 boys :-

( $\frac{8}{x}$ +  $\frac{6}{y}$ ) =  $\frac{1}{2}$..            (1)

Total work done  by 6 men and 2 boys :-

($\frac{6}{x}$  + $\frac{2}{y}$ )= $\frac{1}{3}$..          (2)

By multiplying equation (2) with 3, we get:-

 $\frac{18}{x}$ + $\frac{6}{y}$ = $\frac{3}{3}$ = 1..          ( 3)

now (1) -(3) :-

$\frac{8}{x}$ + $\frac{6}{y}$ = $\frac{1}{2}$

$\frac{18}{x}$ + $\frac{6}{y}$ = 1

-   -     -

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

$\frac{8}{x}$ - $\frac{18 }{x}$ = $\frac{1}{2}$ - 1 = - $\frac{1}{2}$

$\frac{8 - 18}{x}$ = - $\frac{1}{2}$

- $\frac{10}{x}$ = - $\frac{1}{2}$

x = 20

putting the value of x in equation (1) , we get :-

( $\frac{8}{x}$ +  $\frac{6}{y}$ ) =  $\frac{1}{2}$

$\frac{8}{20}$ + $\frac{6}{y}$ = $\frac{1}{2}$

$\frac{6}{y}$ = $\frac{1}{2}$ - $\frac{8}{20}$ = $\frac{10 -8}{20}$ = $\frac{2}{20}$ = $\frac{1}{10}$

∴ y = 6 × 10 = 60

1 man can dig the well in = 20 days

∴1 man can do the work in 1 day = $\frac{1}{20}$ part

∴ 5 men can dig a well in = $\frac{1}{20 }$ × 5 = 4 days.

1 boy can dig the well in = 60 days

∴ 1 boy can do in 1 day = $\frac{1}{60}$ part

∴3 boys can dig a well in = $\frac{1}{60}$ × 3 = 20 days

Total work done in 1 day = $\frac{1}{20}$ + $\frac{1}{60}$ = $\frac{3 +1}{60}$  = $\frac{4}{60}$ = $\frac{1}{15}$

hence 5 men and 3 boys take to do it in 15 days.

Ans :- 5 men and 3 boys take to do it in 15 days.