Question

eight man and six boys can finish a piece of work in 1day while two men and three boys can finish it in 3days. find the time taken by one men alone and that by one boy alone to finish the work.​

Answer 1

Solution:

Suppose 1 man alone can finish the work in x days and 1 boy alone can finish it in y days. <br> Then , 1 man's 1 day's work =.

1

x

<br> And, 1 boy's 1 day's work =

1

y

<br> 8 men and 12 boys can finish the work in 5 days <br>

( 8 men's 1 day's work ) + ( 12 boy's 1 day's work ) =

1

5

<br>

=> 8 + 12 = 1

x y 5

<br>

=> 8u + 12v = 1

5

... (i), where

1 = u and 1 = v

x y

<br> Again, 6 men and 8 boys can finish the work in 7 days <br>

=>

( 6 men's 1 day's work) + ( 8 boy's 1 day's work)

= 1

7

<br>

=> 6 + 8 = 1

x y 7

<br>

=> 6u + 8v = 1

7

. (ii) <br> On multiplying (i) by 3, (ii) by 4 and subtracting the results, we get <br>

4v = ( 3 - 4 ) = 1 => v = 1

5 7 35 140

<br> On putting

v = 1

140

in (ii), we get <br>

6u = ( 1 - 8 ) = 12 => u = ( 1

7 140 140 140

<br>

=> 1 = 1 => x = 70

x 70

<br>

Therefore, one man along can finish the work in 70 days, <br> and one boy alone can finish the work in 140 days.

HOPE IT HELPS U MY FRIEND...

PLZZ LIKE MY ANSWER AND FOLLOW ME AND MARK ME BRAINLIST.....