# A can do a piece of work in 8 days and B alone can do the same work in 10 days. A and B agreed to do the work together for Rs. 720. With the help of C, they finished the work in 4 days. How much C is to be paid?${ A)\;Rs.72 \\ B)\;Rs.82 \\ C)\;Rs.70 \\ D)\;Rs.{\text{ }}80 \\ }$

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Hint:In this question, we have to find out the wages of C. First, we need to calculate the one day’s work of A and B which can be calculated by simply adding the fractions part of A’s one day work and B’s one day work. Subtract one day’s work of (A+B) from one day’s work of (A+B+C). Convert one day’s work of A, B, and C in the ratio and distribute the said amount to get the share of C.

Given: A can do a piece of work in $8$ days and B alone can do the same work in $10$ days.
Therefore, the above expression can be written as
One day work of A is $\dfrac{1}{8}$ and One day work of B is $\dfrac{1}{{10}}$.
To find C’s one day work, we will find the one-day work for A and B
Therefore, the expression can be written as

Therefore, one day work of C can be written as
${ \dfrac{1}{4} - (\dfrac{1}{8} + \dfrac{1}{{10}}) \\ = \dfrac{1}{4} - \dfrac{9}{{40}} \\ = \dfrac{1}{{40}} \\ }$
Take the ratios of the wages of A, B, and C which can be written as
$\dfrac{1}{8}:\dfrac{1}{{10}}:\dfrac{1}{{40}} = 5:4:1$
Therefore, the ratio is $5:4:1$
Now, C’s share can be calculated as
${ \dfrac{1}{{5 + 4 + 1}} \times 720 \\ = \dfrac{1}{{10}} \times 720 \\ = 72 \\ }$
Therefore, C’s share is Rs.
Hence, answer is Rs. $72$,

So, the correct answer is “Option A”.

Note:To find the individual share when the ratios are given, we must be careful while distributing the amount. Any other method applied to find the individual share will make it more complicated.