Question

4 men n 6 boys can do work in 20 days.the same work is done in 28 days by 3 men n 4 boys. How long would it take to one man and one boy to do work separate
Pls answer fast

Answer 1

Let time taken by one man alone be = x days

Let time taken by one boy alone be = y days

According to question

\frac{4}{x}+\frac{6}{y}=\frac{1}{20} .......(1)

and \frac{3}{x}+\frac{4}{y}=\frac{1}{28} .......(2)

Solve equation (1) and (2) by elimination method

Multiply equation (1) by 2 and equation (2) by 3 then subtract

\frac{8}{x}+\frac{12}{y}=\frac{1}{10} ...... (3)

\frac{9}{x}+\frac{12}{y}=\frac{3}{28} .......(4)

Subtract equation (4) from equation (3)

\frac{8}{x}-\frac{9}{x}+\frac{12}{y}-\frac{12}{y}=\frac{1}{10}-\frac{3}{28}

\frac{-1}{x}=\frac{14-15}{140}

\frac{-1}{x}=\frac{-1}{140}

x=140

so, the time taken by one man alone is 140 days

Put value of x in equation (1)

\frac{4}{140}+\frac{6}{y}=\frac{1}{20}

\frac{2}{70}+\frac{6}{y}=\frac{1}{20}

Subtract both the sides by \frac{2}{70}

\frac{6}{y}=\frac{1}{20}-\frac{2}{70}

\frac{6}{y}=\frac{7-4}{140}

\frac{6}{y}=\frac{3}{140}

Multiply both the sides by \frac{y}{6}

\frac{y}{6} \times \frac{6}{y}=\frac{y}{6} \times \frac{3}{140}

1=\frac{y}{280}

Multiply both the sides by 280,

y=280

so, the time taken by one boy alone is 280 days

Therefore, the time taken by one man alone is 140 and time taken by a boy is280 days.

Answer 2

Answer:

Refers to the attachment