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The cost per unit of electricity during a 4 year period is a

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The cost per unit of electricity during a 4 year period is a  [#permalink]

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New post Updated on: 08 Apr 2014, 01:31
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The cost per unit of electricity during a 4 year period is as follows:

Year 1, $1 per unit;
Year 2, $1.5 per unit;
Year 3, $1.2 per unit;
Year 4, $2 per unit.

If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?

A. $1.333
B. $1.250
C. $1.425
D. $1.175
E. $1.500

Originally posted by Safal on 07 Apr 2014, 22:18.
Last edited by Bunuel on 08 Apr 2014, 01:31, edited 4 times in total.
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Re: Try this out!  [#permalink]

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New post 07 Apr 2014, 22:23
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Let money spent each year = $6

Units bought first year = 6
Units bought second year = 4
Units bought third year = 5
Units bought fourth year = 3

Total number of units = 18
Total money spent = 6*4 = 24

Average = 24/18 = 4/3 = 1.33

Answer is A
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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New post 13 Mar 2015, 11:51
1
[align=]It can be solved by weighted average formula, which is

=( x1*n1+x2*n2+x3*n3+......................)/(n1+n2+n3+...............)

where, x1,x2,x3 are values assigned

and, n1,n2,n3 are the frequency or no. of repetition of x1,x2,x3 respwctively.

As problem states:
x1*n1=x2*n2=x3*n3=x4*n4

LCM of (x i )1,1.5,1.2,and 2 is 6

Therefore n1=6, n2=4, n3=5and n4= 3

Calculating average using above formula
Avg.= 4*6/(6+4+5+3)
= 1.33[/align]
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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New post 15 Feb 2016, 19:55
my approach was to pick a number that would be easy to divide by all the prices given.
suppose company spent 12$ each year.
1st year - used 12 units
2nd year - 8 units
3rd year - 10 units
4th year - 6 units
total, we have 36 units.
since 12$/year was spent, in all 4 years was spent 48$.
now, avg price is total $/total # units = 48/36 = 4/3 or 1.33

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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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New post 15 Feb 2016, 22:01
Safal wrote:
The cost per unit of electricity during a 4 year period is as follows:

Year 1, $1 per unit;
Year 2, $1.5 per unit;
Year 3, $1.2 per unit;
Year 4, $2 per unit.

If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?

A. $1.333
B. $1.250
C. $1.425
D. $1.175
E. $1.500



Here is another method for the more mathematically inclined. When we talk about equal amount of money spent, the average price is the harmonic mean of all the prices.

\(1/1 + \frac{1}{1.5} + \frac{1}{1.2} + \frac{1}{2} = \frac{4}{H}\)

\(\frac{6}{6} + \frac{4}{6} + \frac{5}{6} + \frac{3}{6} = \frac{4}{H}\)

\(H = \frac{4}{3} = 1.333\)

Answer (A)
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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New post 16 Feb 2016, 00:56
1
Safal wrote:
The cost per unit of electricity during a 4 year period is as follows:

Year 1, $1 per unit;
Year 2, $1.5 per unit;
Year 3, $1.2 per unit;
Year 4, $2 per unit.

If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?

A. $1.333
B. $1.250
C. $1.425
D. $1.175
E. $1.500


Hi all,
you cannot apply AVERAGE straightway as the units are not the same for each year, example the expense at $1 is higher than at $2..
Also we cannot apply weighted average as we have four quantities and that too in not proper form..

there can be two ways...

arithmetic way



choose a number, which is LCM of all four, say 6 here..
how much can you purchase
Year 1, $1 per unit; ---- 6/1=6 units
Year 2, $1.5 per unit; -- 6/1.5=4 units
Year 3, $1.2 per unit; -- 6/1.2=5 units
Year 4, $2 per unit. ---- 6/2=3 units...
total units = 6+4+5+3=18 units..
cost incurred = 6*4=24..
avg cost= 24/18=1.333


Weighted average



lets test weighted average for two pairs separately..
also since overall expenditure is same each year, the units will be proportional to cost..

1) $1 and $2..
the ratio of units is 2:1, so the weighted average will be 1+(2-1)* 1/(1+2)= 1.333
2) $1.5 and %1.2..
ratio of units = 1.5:1.2...
so weighted average= 1.2 + 1.5/(1.2+1.5)= 1.2+(1.5-1.2)*1.5/2.7= 1.2 + 3*1.5/27= 1.2+ 1/6= 1.2+ 0.1333= 1.333..

now we have two quantities with the same average rate= 1.333,
so their combined averge rate will also be 1.333


NOTE:- the answer will be lesser than the average of the cost, as while doing so we take the qty at each price to be same, whereas the quantities are higher for lower values..
so average< (1+1.5+1.2+2)/4= 1.425.. you can straight way eliminate C and E..
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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New post 16 Feb 2016, 08:08
VeritasPrepKarishma wrote:
Safal wrote:
The cost per unit of electricity during a 4 year period is as follows:

Year 1, $1 per unit;
Year 2, $1.5 per unit;
Year 3, $1.2 per unit;
Year 4, $2 per unit.

If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?

A. $1.333
B. $1.250
C. $1.425
D. $1.175
E. $1.500



Here is another method for the more mathematically inclined. When we talk about equal amount of money spent, the average price is the harmonic mean of all the prices.

\(1/1 + \frac{1}{1.5} + \frac{1}{1.2} + \frac{1}{2} = \frac{4}{H}\)

\(\frac{6}{6} + \frac{4}{6} + \frac{5}{6} + \frac{3}{6} = \frac{4}{H}\)

\(H = \frac{4}{3} = 1.333\)

Answer (A)


Hi Karishma,
Is there any mathematical principal for this ?
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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New post 16 Feb 2016, 08:54
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1
Safal wrote:
The cost per unit of electricity during a 4 year period is as follows:

Year 1, $1 per unit;
Year 2, $1.5 per unit;
Year 3, $1.2 per unit;
Year 4, $2 per unit.

If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?

A. $1.333
B. $1.250
C. $1.425
D. $1.175
E. $1.500


Since equal dollars is spent on electricity each year we take the LCM of 1, 1.2, 1.5 & 2 ; ie - 6

So, We get the factory spent $6 dollar each year ( Year 1 - Year 4 ), so during the 4 years they spent $ 24

Now, calculate the unit of electricity consumed.

Unit of electricity consumed = Total Cost /Cost per unit of electricity

Now, calculate the consumption Year wise-

Year 1 = 6/1 =>6 units

Year 2 = 6/1.5 => 4 units

Year 3 = 6/1.2 => 5 units

Year 4 = 6/2 => 3 units

Total consumption during the four years is ( 6+4+5+3) 18 units.

We are asked to find -
Quote:
the average cost of a unit of electricity during the 4 year period


Average cost of a unit of electricity = Total cost of electricity during the 4 years / Total Consumption during the 4 years.

Average cost of a unit of electricity = 24 /18 =>1.33

Hence answer is (A)

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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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New post 25 Mar 2016, 18:51
bumped again into this question..started to consider some coefficients for units used..but then...considered 6$ as total spent. I believe this is the LCM of 1, 1.5, 1.2, and 2.
1st year - 6 units
2nd year - 4 units
3rd year - 5 units
4th year - 3 units

total = 18 units. total $ spent = 24$. 24/18 = 4/3 = 1.33
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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New post 15 Mar 2018, 10:09
Safal wrote:
The cost per unit of electricity during a 4 year period is as follows:

Year 1, $1 per unit;
Year 2, $1.5 per unit;
Year 3, $1.2 per unit;
Year 4, $2 per unit.

If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?

A. $1.333
B. $1.250
C. $1.425
D. $1.175
E. $1.500


We can assume the factory spent $18 a year on electricity. Thus, it used

Year 1: 18 units of electricity

Year 2: 12 units of electricity

Year 3: 15 units of electricity

Year 2: 9 units of electricity

Therefore, the average cost per unit is:

(4 x 18)/(18 + 12 + 15 + 9)

72/54

4/3

1.333

Answer: A
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Re: The cost per unit of electricity during a 4 year period is a &nbs [#permalink] 15 Mar 2018, 10:09
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