spent equal dollars

[sanju09]

The cost of 1 unit of electricity during a 4 year period is given below:

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 each year for electricity 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

[spoiler]OA A[/spoiler]

[scoobydooby]

since same amount of money is spent every year we need to compute harmonic mean. if same quantity was spent we would have used arith mean

hm: n/(1/a1+1/a2+1/a3...1/an)

average: 4/(1/1+1/1.2+1/1.5+1/2)
=4/(10/12+10/15+1/2+1)
=4/(50+40+30+60)/60
=4/180/60
=4/3
=1.333 hence A

[lav]

The factory spent equal dollars each year for electricity , let it be x$
Now ques is ...
what was the average cost of a unit of electricity during the 4 year period? Let it be y

y= (total cost)/(total units)
total cost = (4x)
total units = units 1st yr + units 2nd yr + units 3rd yr + units 4th yr
total units = (x/1) + (x/1.5) + (x/1.2) + (x/2)

divide the two , x will cancel from N and D
and you will get ans 4/3 = 1.33333