Name: Linear Equations With One or More Variables
Uploaded: 2019-07-19
Duration: 11 min 20 s
Description: Let's learn the concept of linear equations, the introduction of linear algebra, the formation of linear equations in one, two and three variables, etc.

Question

$8$ men and $12$ boys can finish a piece of work in $10$ days while $6$ men and $8$ boys can finish it in $14$ days. Find the time taken by one man alone and one boy alone to finish the work.

Accepted Answer

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

Since, $8$ men and $12$ boys can finish a piece of work in $10$ days,
$6$ men and $8$ boys can finish it in $14$ days
$\Rightarrow \frac{8}{x} + \frac{12}{y} = \frac{1}{10}$ and $\frac{6}{x} + \frac{8}{y} = \frac{1}{14}$

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

$\Rightarrow 8 a + 12 b = \frac{1}{10}$ $- - - - - - - - - - (i)$ and

$\Rightarrow 6 a + 8 b = \frac{1}{14}$ $- - - - - - - - - - (ii)$

Multiply equation $(i)$ by $3$ and equation $(ii)$ by $4$ ,

$24 a + 36 b = \frac{3}{10}$ $- - - - - - - - (iii)$

$24 a + 32 b = \frac{1}{14} \times 4$

$\Rightarrow 24 a + 32 b = \frac{2}{7}$ $- - - - - - - - - (iv)$

Subtracting equation $(iv) from (iii)$ , we get

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

$4 b = \frac{1}{70}$ $\Rightarrow b = \frac{1}{280}$

Substitute $b$ in equation $(i)$ , we get

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

$\Rightarrow 8 a + \frac{3}{70} = \frac{1}{10}$

$\Rightarrow 8 a = \frac{1}{10} - \frac{3}{70}$

$\Rightarrow 8 a = \frac{7 - 3}{70} = \frac{4}{70}$

$\Rightarrow a = \frac{4}{70} \times \frac{1}{8} = \frac{1}{140}$

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

Hence, one man can finish work in $140$ days and one man can finish work in $280$ days.

$8$ men and $12$ boys can finish a piece of work in $10$ days while $6$ men and $8$ boys can finish it in $14$ days. Find the time taken by one man alone and one boy alone to finish the work.

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and one boy alone to finish the work.

Important Questions on Pair of Linear Equations in Two Variables

Learn and Prepare for any exam you want !

$8$ men and $12$ boys can finish a piece of work in $10$ days while $6$ men and $8$ boys can finish it in $14$ days. Find the time taken by one man alone and one boy alone to finish the work.