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: In above question we need to add mixed fractions. For this we will convert mixed fraction into improper fraction.
Then after taking LCM of all the denominators we will add them. Multiply the total time with the given rate to find his earnings.

Complete step-by-step answer:
It is given that a boy is working for 6 consecutive days.
Following are the working duration of him.
 $ {T_1} = 8hrs;{T_2} = 7\dfrac{1}{2}hrs;{T_3} = 8\dfrac{1}{4}hrs $
\[{T_4} = 6\dfrac{1}{4}hrs;{T_5} = 6\dfrac{3}{4}hrs;{T_6} = 7hrs\]
First we will add all the working hours of boy
Total working hours of boy
 $ \Rightarrow T = {T_1} + {T_2} + {T_3} + {T_4} + {T_5} + {T_6} $
 $ \Rightarrow T = \left[ {8 + 7\dfrac{1}{2} + 8\dfrac{1}{4} + 6\dfrac{1}{4} + 6\dfrac{3}{4} + 7} \right] $
 $ \Rightarrow T = \left[ {8 + \dfrac{{15}}{2} + \dfrac{{33}}{4} + \dfrac{{25}}{4} + \dfrac{{27}}{4} + 7} \right] $
 $ \Rightarrow T = \left[ {\dfrac{{16 + 15}}{2} + \dfrac{{33 + 25 + 27 + 28}}{4}} \right] $
 $ \Rightarrow T = \left[ {\dfrac{{31}}{2} + \dfrac{{113}}{4}} \right]hrs $
 $ \Rightarrow T = \dfrac{{62 + 113}}{4} = \left( {\dfrac{{175}}{4}} \right)hrs $
Now we will multiply hours with payment per unit hour.
Payment per unit hour $ = $ 36 Rs
So payment for $ \dfrac{{175}}{4}hrs = \left( {\dfrac{{175}}{4} \times 36} \right) $
 $ = \left( {175 \times 9} \right)Rs $
 $ = Rs.1575/ - $
Therefore he will earn Rs. 1575/- from his work.

Note: 1. It is to be noted that when mixed fractions are given we should convert them in simple fractions before performing any operation like addition or subtraction.
2. When we multiply any fraction, the only numerator is to be multiplied with that number.