Question

John gets Rs 57 per hour of regular work and Rs 114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?

• A. 12
• B. 14
• C. 15
• D. 21

Answer 1

The Correct Option is A

To solve the problem, let's define the variables for regular and overtime work:

x = hours of regular work

y = hours of overtime work 

Given:

• John's hourly rate for regular work = Rs 57
• John's hourly rate for overtime work = Rs 114
• Total hours worked = 172
• Income from overtime work is 15% of income from regular work

From these facts, we have the following equations:

1. Total hours equation: \(x + y = 172\)
2. Income equation: \(114y = 0.15 \times 57x\)

First, let's solve the income equation:

\[114y = 0.15 \times 57x\]

\[114y = 8.55x\]

From the income equation, we can express \(y\) in terms of \(x\):

\[y = \frac{8.55}{114}x\]

Simplify:

\[y = 0.075x\]

Now, substitute \(y = 0.075x\) into the total hours equation:

\[x + 0.075x = 172\]

\[1.075x = 172\]

Solve for \(x\):

\[x = \frac{172}{1.075}\]

\[x = 160\]

Now, using \(x = 160\), find \(y\):

\[y = 0.075 \times 160\]

\[y = 12\]

So, John worked 12 hours of overtime. Hence, the correct answer is:

12