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The average wages of a worker during a fortnight comprising 15 consecu

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The average wages of a worker during a fortnight comprising 15 consecu  [#permalink]

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New post 13 Mar 2016, 12:44
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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?

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

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Re: The average wages of a worker during a fortnight comprising 15 consecu  [#permalink]

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New post 13 Mar 2016, 19:37
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
Answer D

Alternatively ,
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

Answer D
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Re: The average wages of a worker during a fortnight comprising 15 consecu  [#permalink]

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New post 13 Mar 2016, 20:56
Bunuel wrote:
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?

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


Hi,

Ofcourse calculation of averages and subtraction etc here is not very cumbersome..

But another approach which cuts down on calculations and could help in some other Q of same type with cumbersome calculations..

Solution-
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 average is 87+2.5= 89.5 for these 14 numbers..
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

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Re: The average wages of a worker during a fortnight comprising 15 consecu  [#permalink]

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New post 13 Mar 2016, 21:12
Total wages = 15*90 -- (1)
Total wages excluding the 8th day= 7(87+92) = 7*179-- (2)
The difference between 1 and 2 should end in 7.
Hence D.
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Re: The average wages of a worker during a fortnight comprising 15 consecu  [#permalink]

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New post 13 Mar 2016, 21:22
Bunuel wrote:
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?

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

First 7 days the worker gets $3 less than average and the last 7 days the worker gets $2 more than the average.
Hence during these 14 days the net change is negative $7.
Therefore, on the 8th he has to get $97.
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Re: The average wages of a worker during a fortnight comprising 15 consecu  [#permalink]

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New post 14 Mar 2016, 12:00
Bunuel wrote:
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?

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


short cut only applicable for similar problem to save calculation time (in case we have tedious calc) => since total wage will be product of \(90 * 15\) it will always end with 0, and 8th day wage =\(TOTAL - 1st 7day - last 7 days\) or \(Total - (1st 7days + last 7 days)\)we can only do summation of products of Unit digits of 7 days and subtract the unit digit from 10, any option with that number is candidate answers.

1st 7 days = 7*7 = unit digit 9
last 7 days = 2*7 = unit digit 4

Unit digit of summation of these two = 3

So possible answer must end with 7 as unit digit, only possible answer is D


Large method
total 15 day of wages =>\(15*90 = 1350\)
1st 7 days wages =>\(7*87 = 609\)
last 7 days of wages =>\(7*92 = 644\)

8th day wage => \(1350 - 609 - 644 = 97\)
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Re: The average wages of a worker during a fortnight comprising 15 consecu  [#permalink]

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New post 04 Jan 2018, 16:46
Hi All,

We're told that the average pay a worker received for 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. We're asked for his wage on the 8th day.

There are a number of different ways to approach the 'math' in this question. Here's an approach that allows you to avoid a lot of 'step-heavy' math and focus on the 'relationships' between the numbers.

Since the average pay was $90/day, we can track how much 'below average' or 'above average' the individual days are...
-For the first 7 days, the average pay was $87/day, thus each of those days was $3 BELOW the average... meaning that we're (7)($3) = $21 'below' in total here.
-For the last 7 days, the average pay was $92/day, thus each of those days was $2 ABOVE the average... meaning that we're (7)($2) = $14 'above' in total here.

With those 14 days, we're a total of '$7 below' what the average is supposed to be, so that final day (the 8th day) has to make up for that difference...

8th day = $90 + $7 = $97

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Re: The average wages of a worker during a fortnight comprising 15 consecu   [#permalink] 04 Jan 2018, 16:46
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