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

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)

[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]

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

A.

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 -

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)

Responding to a pm:


Harmonic mean is a kind of average. In situations where same amount of money is spent on items with different costs, HM is used.

When you need to average prices a, b and c:

\(HM = \frac{N}{1/a + 1/b + 1/c}\)

N is the total number of elements for which you need to find the average.

Now consider that you spent equal amount of money $D all four years at diff rates

Average Rate = Total money/Total units consumed

Total number of units consumed = D/a + D/b + D/c

Total money = 3*D

Average rate = \(\frac{3D}{D/a + D/b + D/c} = \frac{3}{1/a + 1/b + 1/c}\)

This is the same as the calculation of HM. Hence, we can do it directly if we know where to use it.

Let the company spent $60 each year [LCM of 10, 15, 12, and 20]

Year 1: \(\frac{60}{ 1}\) = 60 units

Year 2: \(\frac{60}{ 1.5}\) = 40 units

Year 3: \(\frac{60}{ 1.2}\) = 50 units

Year 4: \(\frac{60}{ 2}\) = 30 units

Total units: 60 + 40 + 50 + 30 = 180

Total money spent: 60 * 4 = 240

Average: \(\frac{240 }{ 180}\) = \(\frac{4 }{ 3}\) = 1.33

Answer A

Hi Karishma,
Is there any mathematical principal for this ?

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

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

Since the factory spent equal dollars on electricity each year ,
let x dollar be the amount spent.
So in the first year :-
dollar spent = x $
unit bought= x

in the second year :-
dollar spent = x$
units bought = x/1.5 ( Since 1.5 dollar can buy 1 unit ; 1 dollar can buy 1/1.5 unit ; x dollar can buy x/1.5 units )

in the third year :-
dollar spent = x$
units bought = x/1.2

in the fourth year :-
dollar spent = x$
units bought = x/2

Total money spent = 4*x $

Total units bought = x + x/1.5 + x/1.2 + x/2 = 3*x units

Now,
3*x units cost you 4*x $
1 unit costs you 4*x / 3*x = 4/3 dollar = 1.33 dollar

So , the average cost of a unit of electricity during the 4 year period = 1.333 dollar
Option A is the answer.
Please give me kudo s if you liked my explanation.

We're told the factory spent equal dollars on electricity each year. Lets say that amount is $6 each year.

Year 1: 6 units
Year 2: 4 units
Year 3: 5 units
Year 4: 3 units

Total: 18 units
Total amount spent $24

$24/18 = 1.333

Answer is A.

Pick a $$ amount for the yearly amount spent on electricity. Get used to doing this. Many many problems require this kind of thing. $100 is a good amount. So over 4 years $400 will be spent. Divide the unit costs into the $100 to get units of electricity purchased. you should get that 100+66+83+50 units of electricity were purchased, so basically 300 units. Then $400/300 units = $4/3units = $1.33 per unit A

If you find my explanation to be helpful, PLEASE GIVE ME KUDOS

­For a more mathmatical approach, took me moment to figure this out.
Let Y be the amount spent per year, and let u_i be the number of unit spend on i year.

Y = u_1 * $1/unit
Y = u_2 * $1.5/unit
Y = u_3 * $1.2/unit
Y = u_4 * $2/unit

The total number of units spent will then be
u_1 + u_2 + u_3 + u_4 = Y/1 + Y/1.5 + Y/1.2 + Y/2 = 18Y/6 units = 3Y units
Total Spent = 4Y, Since Y is the amount you spend per year.

Average Cost = Total Spent / Total number of Unit
Average Cost = 4Y / 3Y  = 1.333

Thus $1.333/unit is the average cost. This question was really confusing.