Question

4 men and 4 boys can do a piece of work in 3 days.While 2men and 5 boys can finish it in 4 days.How long would it take for 1 boy to do it? How long would it take for 1 men to do it?

Answer 1

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$\underline{\underline{\huge{\textbf{Solution:}}}}$:

Given,

Statement - I :
4 men and 4 boys can do a piece of work in 3 days.

Statement - II :
2men and 5 boys can finish it in 4 days.How

$\underline{\large{\textsf{Step-1}}}$:
Express the given Statements in terms of variables

Let Amount of work done by a man in one day be M
and Amount of work done by a boy in one day be B

$4M + 4B = \frac{1}{3}$

$2M + 5B = \frac{1}{5}$

$\implies 12M + 12B = 1$ ------------(1)

$\implies 8M + 20B = 1$ ------------(2)

It is clear from the both the statements that,
It takes 12 men days and 12 boy days to finish a piece of work and it takes 8 men days and 20 boy days to finish the same piece of work.

$\underline{\large{\textsf{Step-2}}}$:
Find the relation between the work done by a Man and work done by a boy in one day

Equate (1) and (2)

$\implies 12M + 12B = 8M + 20B$

$\implies 12M - 8M = 20B - 12B$

$\implies 4M = 8B$

$\implies M = 2B$ ---------(3)

$\therefore$ Work done by a single man in one day is twice as work done by a single boy in one day

$\underline{\large{\textsf{Step-3}}}$:
Find the No. of days taken by a single boy to finish the piece of work

Substitute (3) in (1) to get value of another variable

$\implies 12(2B) + 12B = 1$

$\implies 24B + 12B = 1$

$\implies 36B = 1$

$B = \frac{1}{36}$ --------(4)

$\therefore$ It takes a single boy 36 days to finish the piece of work .

$\underline{\large{\textsf{Step-3}}}$:
Find the No. of days taken by a single men to finish the piece of work

From(3) , $M = 2B$

Substitute the value of B

$\implies M = 2(\frac{36}{2})$

$\implies M = \frac{1}{18}$

$\therefore$ It takes a single man 18 days to finish the piece of work .

$\therefore$

$\star \textsf{It takes 36 days for single boy to do the work}$

$\star \textsf{It takes 18 days for single man to do the work}$

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