Question

2 men and 5 boys can do a piece of work in 4 days. The same work is done by 3 men
and 6 boys in 3 days. . Find the time taken by 1 man alone and by 1 boy alone to finish
the work.​

Answer 1

Let the amount of work done by a Man alone in a day be M and by a Boy alone be B

Given, 2 men and 5 boys together can finish a piece of work in 4 days

Amount of work they can do in one day 2M+5B =

1/4 -- (1)

Similarly, 3M+6B= 1/3 --- (2)

Solving equations (1) and (2), we get B= 1/36

Substituting B in equation (2), we get M= 1/18

Hence, one man alone will take 18 days to do the work and one boy will take 36 days.

Answer 2

Given:

✭ Time taken by 2 men and 5 boys to complete the work =4 days

✭ Time taken by 3 men and 6 boys to complete the work = 3 days

To Find:

◈ Time taken by one man and one boy alone to complete the work,

Solution:

Let the time taken by a man alone to complete the work be x days

Let the time taken by a boy alone to complete the work be y days.

By given,

⪼ 2/x + 5/y =1/4---(1)

In the second case,

⪼ 3/x + 6/y = 1/3---(2)

Let 1/x =p, 1/y = q

Hence equation 1 and 2 changes to

➠ 2p + 5q = 1/4---(3)

➠ 3p + 6q = 1/3---(4)

Multiply equation 3 by 3 and 4 by 2

➢ 6p + 15q = 3/4

➢ 6p + 12q = 2/3

Solving by elimination method,

»» 3q = 3/4 - 2/3

»» 3q = 9/12 - 8/12

»» 3q = 1/12

»» q = 1/36

We know that 1/y = q, y = 1/q , y = 36

Hence a boy takes 36 days to complete the work

Substitute value of q in equation 4

➳ 3p + 6/36 = 1/3

➳ 3p + 1/6 = 1/3

➳ 3p = 1/3 - 1/6

➳ 3p = 1/6

➳ p = 1/18

Also 1.x = p, x = 1/p, x = 18

Hence a man takes 18 days to complete the work.

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