Question

2 men and 5 boys can finish a piece of work in 4 days, while 3 men
and 6 boys can finish it in 3 days. Find the time taken by one man
alone to finish the work and that taken by one boy alone to finish the
work.

Answer 1

Given :

➡ no. of men can finish a piece of work in 4days=2

➡ no. of boys can finish a piece of work in 4 days =5

and 6 boys can finish in 3days

To find :

➡ The time taken by one man alone to finish the work

➡ The time taken by one boy alone to finish the work.

Solution :

$\red\bigstar$ Let the amount of work done by a man alone in a day be M and by a Boy

alone be B.

$\red\bigstar$ Given 2men and 5 boys together can finish a piece of work in 4days.

$\\ \to \bf \: amount \: of \: work \:they \: can \: do \: in \: one \: day \:$

$\sf{2M+5B=\dfrac{1}{4}}$ ......(1)

Similarly, $\sf{ 3M+6B=\dfrac{1}{3}}$......(2)

Solving both equations (1) and (2) we get

$\blue\bigstar\bf{ B=\dfrac{1}{36} \: }$

Substitute this values in equation (1) we get,

$\blue\bigstar\bf{M=\dfrac{1}{18}}$

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