Question

8 men and 12 boys can do a pieces of work in 10 days while 6 men and 8 boys can finish it in 14 days find the time taken by one man and one boy to finish the work​

Answer 1

Let the part of the job done by 1 men per day be x

Let the part of the job done by 1 boy per day be y

So,

Multiply equation 1 by 3 and equation 2 by 4 to get,

From equation 3 and 4,

So the time taken by the boy to complete the job alone will be 280 days and for the men will be 140.

Answer 2

Answer:

140 days.

Step-by-step explanation:

Let the time be taken by one man to complete the work be x and time taken by one boy to complete $\frac{1}{y}$ part of the work.

Since 8 men and 12 boys can finish a piece of work in 10 days,

⇒$\frac{8}{x}+\frac{12}{y} =\frac{1}{10}$ and $\frac{6}{x} +\frac{8}{y}=\frac{1}{14}$

Since the equations are not linear, let $\frac{1}{x}=a$ and $\frac{1}{y}=b$

⇒$8a+12b=\frac{1}{10}$ and $6a+8b=\frac{1}{14}$

Multiply the first equation by 3 and second equation by 4, we get

$24a+36b-24a-32b=\frac{3}{10}$ and $24a+32b=\frac{2}{7}$

Subtract the equations obtained.

$24a+36b-24a-32b=\frac{3}{10}-\frac{2}{7}$

$4b=\frac{1}{70}$⇒$b=\frac{1}{280}$

Substitute in equation $8a+12b=\frac{1}{10}$ to obtain the value of $a$

$8a+12(\frac{1}{280})=\frac{1}{10}$⇒$a=\frac{1}{140}$

So, $x=\frac{1}{a}=140$ and $y=\frac{1}{b}=280$

Hence, a man can finish the work in 140 days.