Question

A worker in a factory is paid Rs x per hour for normal work and double this rate for overtime work. Find the total earning ‘E’ in rupees of a worker who works for 20 hours out of which y hours is the overtime.
A. x(20 –y) – xy
B. x(20 – y) + xy
C. x(20 – y) + 2xy
D. x(20 – y) – 2xy

Answer 1

Hint: Here, we are to find a linear equation based on the given statement for the total earning. In the above question we have normal working rate is Rs x, Overtime working rate is Rs 2x and Total working hour that is 20 hours out of which Overtime working hour is y hours. Now, normal working hours must be (20 – x). We can easily find total earnings by multiplying normal working hours with normal working rates and Overtime working hours with Overtime working rates.

Complete step-by-step answer:
Given, normal working rate of a worker = Rs x
Also given, the overtime rate is double the normal rate.
Therefore, overtime working rate of a worker = Rs 2x (Double of the normal working rate)
Total working hour = 20 hours
Overtime working hours of a worker = y hours
Thus, the normal working hours of a worker = Total working hours – Overtime working hours
                                                                                = (20 – y) hours
Total earning ‘E’ of a worker = (Normal working rate X Normal working hours) + (Overtime working rate and Overtime working hours)
                                                   = x (20 – y) + 2x(y)
                                                   = x (20 – y) + 2xy
Thus, total earning that is ‘E’ is x (20 – y) + 2xy

So, the correct answer is “Option C”.

Note: In these types of questions, we have to form a linear equation based on given statements in question. In the above question you have to keep in mind that Normal working rates should be multiplied by normal working hours and Overtime working rates should be multiplied by Overtime working hours.