Sharing the money for work — lesson. Mathematics State Board, Class 8.

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A group of people work together, and they get a share of money for the work they do is called as sharing the money for the work.

$A$ and

$B$ do work in

$x$ and

$y$ days, respectively, then the ratio of the work done by

$A$ and

$B$ is equal to the ratio of their wages. That is,

$\frac{1}{x} : \frac{1}{y} = y : x$

$A$ ,

$B$ and

$C$ do the same work in

$x$ ,

$y$ and

$z$ days, respectively, their share of money is calculated in the ratio

$\frac{1}{x}:\frac{1}{y}:\frac{1}{z}$ .

Example:

$A$ can finish a work in

$10$ days,

$B$ can finish a work in

$15$ days, and

$C$ can finish a work in

$20$ days. All three worked together and earned a salary of

$₹6500$ . Find the amount of money earned by

$A$ ,

$B$ and

$C$ .

Solution:

Given:

$A$ can finish a work in

$10$ days.

$B$ can finish a work in

$15$ days.

$C$ can finish a work in

$20$ days.

The ratio of the work done by

$A$ ,

$B$ and

$C$ is equal to the ratio of their wages.

Thus, we have:

$\frac{1}{10} : \frac{1}{15} : \frac{1}{20} =$

$\frac{6}{60} : \frac{4}{60} : \frac{3}{60}$

$= 6 : 4 : 3$

The total parts

$= 6 + 4 + 3 = 13$

$A$ 's share

$= \frac{6}{13} \times 6500 = ₹3000$

$B$ 's share

$= \frac{4}{13} \times 6500 = ₹2000$

$C$ 's share

$= \frac{3}{13} \times 6500 = ₹1500$

Therefore, the shares of

$A$ ,

$B$ and

$C$ are

$₹3000$ ,

$₹2000$ and

$₹1500$ respectively.

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2. Sharing the money for work

Theory: