Question

A man’s basic pay for a 40-hour week is Rs 20. Overtime is paid for at $25\%$ above the basic rate. In a certain week, he worked overtime and his total wage was Rs. 25. He, therefore, worked for:
(a) 45 hr
(b) 48 hr
(c) 47 hr
(d) 50 hr

Answer 1

Hint: First of all, we are going to find the man’s basic rate per hour by dividing Rs 20 by 40hours. After that, we are going to find the overtime rate per hour which we will find by first of all multiplying the basic rate per hour by $\dfrac{25}{100}$ then we will add the basic pay rate to it. After we will get the overtime basic rate per hour then we will assume x hours are the number of hours in which man overworked so that his wage becomes Rs 25 so multiplying x by the basic overtime rate per hour and then add this multiplication to Rs 20 and equate this addition to Rs 25. Solve this equation and get the value of x.

Complete step by step answer:
In the above problem, it is given that a man’s basic pay for a 40-hour week is Rs 20 so we are going to find the basic pay rate per hour by dividing Rs 20 by 40 and we get,
$\begin{align}
  & \dfrac{20}{40} \\
 & =\dfrac{1}{2}hrs/week \\
\end{align}$
Now, we are going to find the overtime basic rate per hour by first of all multiplying $\dfrac{1}{2}$ by $\dfrac{25}{100}$ then we will add $\dfrac{1}{2}$ into it.
$\dfrac{1}{2}\times \dfrac{25}{100}+\dfrac{1}{2}$
Taking $\dfrac{1}{2}$ as common from the above expression we get,
$\begin{align}
  & \Rightarrow \dfrac{1}{2}\left( \dfrac{25}{100}+1 \right) \\
 & =\dfrac{1}{2}\left( \dfrac{25+100}{100} \right) \\
 & =\dfrac{1}{2}\left( \dfrac{125}{100} \right) \\
 & =\dfrac{5}{8} \\
\end{align}$
Now, let us assume that the man worked for x hours as overtime so we are going to multiply x by $\dfrac{5}{8}$ and adding Rs 20 to the multiplication and we get,
$x\times \dfrac{5}{8}+20$
Equating the above expression to Rs 25 we get,
$\Rightarrow x\times \dfrac{5}{8}+20=25$
Subtracting 25 on both the sides of the above equation we get,
$\begin{align}
  & \Rightarrow x\times \dfrac{5}{8}=25-20 \\
 & \Rightarrow x\times \dfrac{5}{8}=5 \\
\end{align}$
In the above equation, 5 will be canceled out from both sides and we get,
$\Rightarrow \dfrac{x}{8}=1$
Multiplying 8 on both the sides of the above equation we get,
$x=8$
Now, the total hours that man worked is the addition of 8 hours and 40 hours so the total hours is equal to:
$\begin{align}
  & \left( 40+8 \right) \\
 & =48hr \\
\end{align}$

So, the correct answer is “Option b”.

Note: The mistake which could be possible in the above problem is that you might multiply the assumed x hours of overtime by Rs 20 so make sure you have multiplied the x hours of overtime by $\dfrac{1}{2}$ which is the basic rate per hour. And do mindfulness during calculations because there is a tendency to make mistakes.