Question

4 men and 6 boys can finish a piece of work in 20 days,while 3 men and 4 boys can finish it in 28 days.find the time tsken by one man alone and that by one boy alone to finish that work

Answer 1

Answer:

The time taken by one man alone is 140 days and the time taken by one boy alone is 280 days .

Step-by-step explanation:

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 eliminating,

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 days and the time taken by one boy alone is 280 days .

Answer 2

Answer:

Step-by-step explanation:

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.