Question: The average wages of a worker during a fortnight comprising 15 consecutive 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?

1. $83
2. $90
3. $92
4. $97
5. $104

“The average wages of a worker during a fortnight comprising 15”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:
Average daily wage of a worker for 15 consecutive working days = 90$

During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 92$

Wage on 8th day = 90*15 -( 87*7 + 92 *7)
= 1350 - (609 + 644)
=1350 - 1253
= 97

Correct Answer: D

Approach Solution 2:
During the first 7 days , since the daily average daily wage = 87$
Amount by which sum of first 7 days varies from average for entire 15 days = -3*7 = -21

During the last 7 days , since the daily average daily wage = 92$
Amount by which sum of last 7 days varies from average for entire 15 days = 2*7 = 14
Amount by which sums first 7 and last 7 days varies from average for entire 15 days = -21 +14 = -7

Therefore , in order to make average for entire 15 days to be 90 , the wage on 8th day needs to be = 90 + 7 = 97

Correct Answer: D

Approach Solution 3:
we are given averages for 7 days on either side..
the average of these 7+7 days can be easily found out as
92-87=5 so 5/2=2.5 from each number..
so the average is 87+2.5= 89.5 for these 14 numbers..
the 15th number increases this by 90-89.5=0.5..
so 15th number= the final average + increase required in other 14 numbers= 90+14*(90-89.5)=90+14*0.5=90+7=97

Correct Answer: D

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