Arithmetic

Averages

Medium

A car owner buys petrol at the rate ₹ 17, ₹ 19 and ₹ 20 per litre, respectively for three consecutive years. Compute the average cost per litre, if he spends ₹ 6,460 per year for the three consecutive years.

₹ 18.49

₹ 18.58

₹ 19.20

₹ 21.66

✅ Correct Option: 2

Let $x, y$ and $z$ be the no. of litres purchased in three consecutive years, respectively.

Years	1	2	3
No. of litres	x	y	z
Rate	17	19	20
Total Expense	6460	6460	6460

From the above table,

$x = \dfrac{6460}{17} = 380$

$y = \dfrac{6460}{19} = 340$

$z= \dfrac{6460}{20} = 323$

Thus, the average cost per litre $= \dfrac{\text{Total expense}}{\text{Total No. of litres}} = \dfrac{6460 + 6460 + 6460}{380 + 340 +323}$

$= \dfrac{3 \times 6460}{1043} = \dfrac{19380}{1043} = \dfrac{19.38}{1.043}$

From here, we understand that the average has to be lower than $₹ 19.38$ . However, we still have two options, $₹18.49$ or $₹18.58$

To get a unique answer, let's assume the average is $₹18.5$

Thus, total expense $= 18.5 \times 1043 = ₹ 19295.5$ which is lower than actual expense of $₹ 19380$

Hence, the average is greater than $18.5$ , which gives us $18.58$ as the unique solution.

Hence, the correct option is Option 2.

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A car owner buys petrol at the rate ₹ 17, ₹ 19 and ₹ 20 per litre, respectively for three consecutive years. Compute the average cost per litre, if he spends ₹ 6,460 per year for the three consecutive years.

Solution

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