The average wages of a worker during a fortnight comprising 15 consecutives working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $92 per day. What was his wage on the 8th day?

A. $83
B. $90
C. $92
D. $97
E. $104

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

Hi Swerve,
Let's take a look at your question.

The wages of a worker during a fortnight comprising 15 consecutive working days = $90 per day
We know that,
$$Average\ \ =\ \frac{Sum}{Days}$$
$$Sum\ =\ Average\ \times\ Days$$
$$Sum\ =\ 90\ \times15\ =\ 1350$$
Therefore,
Sum of wages of 15 days = $1350

Next the question states that During the first 7 days, his average wages was $87 per day.
Again using the average formula, we will find the sum of wages of first 7 days.
$$Average\ \ =\ \frac{Sum}{Days}$$
$$Sum\ =\ Average\ \times\ Days$$
$$Sum\ =\ 87\ \times7\ =\ 609$$
Therefore,
Sum of wages of first 7 days = $609

Next the question states that he average wages during the last 7 days was $92 per day.
Again using the average formula, we will find the sum of wages of last 7 days.
$$Average\ \ =\ \frac{Sum}{Days}$$
$$Sum\ =\ Average\ \times\ Days$$
$$Sum\ =\ 92\ \times7\ =\ 644$$
Therefore,
Sum of wages of last 7 days = $644

We need to find the wage on 8th day.
We know that,
Sum of wages of first 7 days + Wage on 8th day + Sum of wages of last 7 days = Sum of wages of 15 days
Plugin in all the known wages we calculated above,
609 + Wage on 8th day + 644 = 1350
Wage on 8th day + 609 + 644 = 1350
Wage on 8th day + 1253 = 1350
Wage on 8th day = 1350 - 1253
Wage on 8th day = 97
The wage on 8th day is $97.

Therefore, Option D is true.

Hope it helps.
I am available if you'd like any follow up.