Question

A car owner buys a petrol car at Rs.750 and Rs.8 and Rs.8.50 per liter for three successive years. What approximately is the average cost per liter of petrol if he spends 4000 each year?
$
  (a){\text{ Rs}}{\text{.7}}{\text{.98}} \\
  (b){\text{ Rs}}{\text{.8}} \\
  (c){\text{ Rs}}{\text{.8}}{\text{.50}} \\
  (d){\text{ Rs}}{\text{.9}} \\
$

Answer 1

Hint – In this question first compute the total liters of petrol that he brought in for a total of Rs. 4000 per year with prices of petrol fluctuation per year. For example, the number of liters he bought in the first year = $\dfrac{{4000}}{{7.50}}$ liters. Similarly the number of liters for each year can be calculated. To find the average use the concept that the average cost per liter of petrol is the ratio of total rupees spent in all three years to the total number of liters he bought in these years.

Complete step-by-step answer:
It is given that a car owner spends Rs. 4000 each year on petrol.
In the first year he buys petrol at the rate of 7.50 Rs.
So the number of liters he bought in the first year is the ratio of total rupees spent in that year to the price of 1 liter petrol.
Therefore the number of liters he bought in the first year = $\dfrac{{4000}}{{7.50}}$ liters.
Now in his second year he buys petrol at the rate of 8 Rs.
So the number of liters he bought in the second year is the ratio of total rupees spent in that year to the price of 1 liter petrol.
Therefore the number of liters he bought in second year = $\dfrac{{4000}}{8}$ liters.
And in the third year he buys petrol at the rate of 8.50 Rs.
So the number of liters he bought in the third year is the ratio of total rupees spent in that year to the price of 1 liter petrol.
Therefore the number of liters he bought in third year = $\dfrac{{4000}}{{8.50}}$ liters.
Now the average cost per liter of petrol is the ratio of total rupees spent in all three years to the total number of liters he bought in these years.
So, average cost per liter of petrol is = $\dfrac{{4000 + 4000 + 4000}}{{\dfrac{{4000}}{{7.50}} + \dfrac{{4000}}{8} + \dfrac{{4000}}{{8.50}}}}$
Now simplify this we have,
$ \Rightarrow \dfrac{{1 + 1 + 1}}{{\dfrac{1}{{7.50}} + \dfrac{1}{8} + \dfrac{1}{{8.50}}}} = \dfrac{3}{{0.1333 + 0.125 + 0.1176}} = \dfrac{3}{{0.3759}} = 7.98$ Rs.
So this is the required average cost per liter of petrol in three years.
Hence option (A) is the correct answer.

Note – The average of any set can be taken out as the sum of the average of the total numbers divided by the total numbers present in the set, for example for any set S with n elements $S = \left\{ {{x_1},{x_2},{x_3}............{x_n}} \right\}$will be $Avg = \dfrac{{{x_1} + {x_2} + {x_3} + .........{x_n}}}{n}$. This same concept is extended to this particular problem statement in which ${\text{average cost of petrol = }}\dfrac{{{\text{total cost of petrol in 3 years}}}}{{{\text{cost of petrol in each year}}}}$.