Question

A car owner buys petrol at $Rs.7.50$, $Rs.8.00$ and $Rs.8.50$per liter for three successive years. What approximately is the average cost per liter of petrol, if he spends $Rs.4000$ each year?
\[\begin{align}
  & \left( a \right)Rs.7.98 \\
 & \left( b \right)Rs.8 \\
 & \left( c \right)Rs.8.5 \\
 & \left( d \right)Rs.9 \\
\end{align}\]

Answer 1

Hint: In this question, we are given an amount spent by a person on petrol each year. Also, we are given the rate at which he bought petrol for three years. We have to find the average cost per liter of petrol. Average cost will be calculated by using formula –
$Average~cost=\dfrac{Total~amount~spent}{Total~petrol~consumed}$
As we know the amount spent for one year, so we will calculate the total amount spent for three years. For calculating total petrol consumed, we need to calculate total petrol consumed in each year and then add them to get the total petrol consumed. Formula for calculating liters of petrol consumed in a particular year will be equal to the total amount spent that year divided by the price of petrol per liter.

Complete step-by-step answer:
Here, we are given –
For the first year, the amount of petrol per liter $=Rs.7.50$ per liter.
Total amount spent by the man in this year $=Rs.4000$
For the second year, the amount of petrol per liter $=Rs.8$ per liter.
Total amount spent by the man in this year $=Rs.4000$
For the third year, the amount of petrol per liter $=Rs.8.50$ per liter.
Total amount spent by the man in this year $=Rs.4000$
We need to calculate cost per liter of petrol, which is given by - $\dfrac{Total~amount~spent}{Total~petrol~consumed}$
As we know the amount spent by him in the first, second and third year. Hence, total amount spent becomes $4000+4000+4000=Rs.12000$
Now we need to find the total liters of petrol consumed.
Liters of petrol consumed in any year = $\dfrac{amount~spent~in~that~year}{amount~of~petrol~per~liter}$
Therefore,
For $1st$ year, quantity of petrol consumed $=\dfrac{4000}{7.50}=\dfrac{400000}{750}=533.33l$
For $2nd$ year, quantity of petrol consumed $=\dfrac{4000}{8}=\dfrac{4000}{8}=500l$
For $3rd$ year, quantity of petrol consumed $=\dfrac{4000}{8.50}=\dfrac{400000}{850}=470.58l$
Hence, total amount of petrol consumed in here years $=533.33+500+470.58=1503.91l$
Now,
Average cost per liter of petrol $\dfrac{Rs.12000}{1503.91l}$
$=Rs.7.98$ per liter

Hence, Average cost per liter of petrol is \[Rs.7.98\].

So, the correct answer is “Option A”.

Note: In this question, students should not directly calculate the average of three items given by adding them and dividing by three, as it will give the wrong answer only because the petrol consumed in all three years was different. Students should carefully perform division when decimal numbers are in the denominator.