Question

8 me n and 6 boys can finish a piece of work in one day while 2 men and 3 boys can finish it in 3 days find the time taken by one men and that one boy to finish the work

Answer 1

Q: 8 men and 6 boys can finish a piece of work in one day while 2men and 3boys can finish it in 3days . find the time taken by 1 men and one boy to finish the work .

let 1 man's 1 day's work = x , and 1 boy's 1 day's
work = y so then ,

8x + 6y = 1 / 1 -----------(1)

2x + 3y = 1 /3 -----------(2)

multiply equation (1) by 2 and eq(2) by 8

16x + 12y = 2 ------------(3)

16x + 24y = 8/ 3 --------(4)

-----------------------------subract.(3) and (4)

- 12y = [ 2 - (8/ 3) ]

-12y = - 2/ 3

y = 2 /36 => y = 1 /18

put value of 'y' in (1) we get

8x + 6 ( 1/ 18 ) = 1/ 1=> 8x = 1 - ( 6/ 18 )

8x = ( 3 - 1 )/ 3 = 2 / 3

8x = 2/ 3 =>x = 2 / 24 => x = 1 /12

(1man + 1boy)' s 1 days work

= [ ( ( 1 × 1) /12 ) + ( (1 × 1 )/ 18 ) ]

= ( 1/ 12) + ( 1/ 18 )

= (18 + 12 )/ 216 = 30 / 216 = 1 / 7.2

therefore, 1 men and 1 boy can finish the work in 7.2 days.

Answer 2

8M + 6B = 1D

2M + 3B = 3D

Since both their work are the same:

(8 x 1)M + (6 x 1)B = (2 x 3)M + (3 x 3)B

8M + 6B = 6M + 9B

8M - 6M = 9B - 6B

2M = 3B

M = 1.5B

Find 1 man and 1 boy in term of boys:

1M + 1B = 1.5B + 1B = 2.5B

Find the amount of work 1 boy can do in a day:

8M + 6B = 1D

8(1.5)B + 6B = 1D

18B = 1D

B = 18D

⇒ 1 day = 1/18 of the work

Find the amount of work 1 man can do in a day:

1M = 1.5B

1M = 18D ÷ 1.5

1M = 12D

⇒ 1 day = 1/12 of the work

Find the amount of days 1 man and I boy need to complete the work:

1 day = 1/18 + 1/12 = 5/36 of the work

5/36 of the work = 1 day

1/36 of the work = 1 ÷ 5 = 1/5 day

36/36 of the work = 1/5 x 36 = 7.2 days

Answer: 1 man and 1 boy will take 7.2 days to complete the work.