Question

If a boy works for six consecutive days for \[8\] hours, $7\dfrac{1}{2}$ hours, $8\dfrac{1}{4}$ hours, $6\,\dfrac{1}{4}$ hours, $6\dfrac{3}{4}$ hours and $7$ hours respectively, how much money will he earn at the rate of $Rs.36$ per hour?

Answer 1

Hint:
Find the total hours that a boy works for six consecutive days. After that multiply the earning rate of a boy per hour with the total hours of a boy works to find the money which was earned by the boy.

Useful Formula: To find the total money earned by the boy for working six consecutive days, multiply the total hours with the earning rate of the boy. That is, Total earning = Total Number of hours $ \times $ earning rate .

Complete step by step solution:
Given that, A boy works for six consecutive days for \[8\] hours, $7\dfrac{1}{2}$ hours, $8\dfrac{1}{4}$ hours, $6\,\dfrac{1}{4}$ hours, $6\dfrac{3}{4}$ hours and $7$ hours respectively, and the rate of money he earned per hour is $Rs.36$.
Earning rate of a boy $ = \,Rs.36$
We want to find the total money a boy will earn.
A boy works for six consecutive days for some particular hours.
To find the total hours that a boy works at six consecutive days, sum the given all working hours of a boy:
Number of hours a boy worked for $6$ days is,
$ \Rightarrow \,8\, + \,7\dfrac{1}{2}\, + \,8\,\dfrac{1}{4}\, + \,6\,\dfrac{1}{4}\, + \,6\,\dfrac{3}{4}\, + \,7$
Simplifying the above equation by converting mixed fraction into improper fraction as follows:
 $ \Rightarrow 8\, + \,\dfrac{{15}}{2}\, + \,\dfrac{{33}}{4}\, + \,\dfrac{{25}}{4}\, + \,\dfrac{{27}}{4}\, + \,7$
Taking L.C.M to the above equation to solve the equation:
$ \Rightarrow 8\,(\,\dfrac{4}{4}\,) + \,\dfrac{{15}}{2}\,(\,\dfrac{2}{2}\,) + \,\dfrac{{33}}{4}\, + \,\dfrac{{25}}{4}\, + \,\dfrac{{27}}{4}\, + \,7\,(\,\dfrac{4}{4})$
Simplify the above equation by multiplying the terms,
$ \Rightarrow \dfrac{{32}}{4}\, + \,\dfrac{{30}}{4}\, + \,\dfrac{{33}}{4}\, + \,\dfrac{{25}}{4}\, + \,\dfrac{{27}}{4}\, + \,\dfrac{{28}}{4}$
In the above equation $4$ is the common factor for all the terms, so take it has common from the equation as follows:
$ \Rightarrow \dfrac{{32 + 30 + 33 + 25 + 27 + 28}}{4}$
Add all the terms in the numerator:
$ \Rightarrow \dfrac{{175}}{4}$
Now, convert the above equation in terms of hours:
$ \Rightarrow 43\,\dfrac{3}{4}{\text{ hours}}$
Number of hours a boy worked for $6$days $ = \,43\,\dfrac{3}{4}$hours.
Now, find the total earning of a boy by multiplying the total hours with earning rate of a boy:
Total earnings $ = $ Number of hours a boy worked $ \times $ Earning rate of a boy
Total earnings $ = \,\dfrac{{175}}{4}$ $ \times $ $36$
Simplify the above equation by multiplying the terms:
Total earnings $ = \dfrac{{6300}}{4}$
Solve the above equation:
Total earnings $ = \,Rs.1575$

Thus, the total earnings of the boy who worked for six consecutive days is $\,Rs.1575$.

Note:
The given hours are in the form of mixed fraction $(7\dfrac{1}{2})$, convert them into improper fraction $(\dfrac{{15}}{2})$ by multiplying $2$ with $7$ and add $1$ with their result. This question or question related to this topic are nothing but advance application of unitary method.