Onion is sold for $5$ consecutive months at the rate of Rs $10,20,25,25$ , and $50$ per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these $5$ months is closest to

$26$

$16$

$18$

$20$

✅ Correct Option: 3

We need to find the average price per kg that the family effectively paid over 5 months.

The family spends:

Same fixed amount for first 3 months

Half that amount for next 2 months

The key insight is: since they spend a fixed amount each month, they buy different quantities depending on the price.

We'll use a clever trick to avoid fractions. Let us choose the fixed amount as the LCM of the first 3 prices.

Finding LCM of 10, 20, 25:

10 = 2 × 5

20 = 2² × 5

25 = 5²

LCM = 2² × 5² = 100

So the family spends Rs 100 in each of the first 3 months, and Rs 50 in each of the last 2 months.

Note: Any fixed amount would work, but LCM makes calculations cleaner!

Using the formula: Quantity = Amount Spent ÷ Price per kg

Month	Price (Rs/kg)	Amount Spent (Rs)	Quantity (kg)
1	10	100	100 ÷ 10 = 10
2	20	100	100 ÷ 20 = 5
3	25	100	100 ÷ 25 = 4
4	25	50	50 ÷ 25 = 2
5	50	50	50 ÷ 50 = 1

Total quantity bought = 10 + 5 + 4 + 2 + 1 = 22 kg

Total amount spent = 100 + 100 + 100 + 50 + 50 = Rs 400

Average price per kg = Total amount spent ÷ Total quantity

Average price = $\tfrac{400}{22} = 18.18$ Rs/kg

Common Mistake: Don't just average the prices $(10+20+25+25+50)÷5 = 26$ Rs/kg

This is wrong because the family bought different quantities each month. When quantities are different, we need a weighted average.

The average expense is approximately Rs 18 per kg.

This approach works because we're calculating the true cost per kg based on actual spending patterns, not just arithmetic mean of prices.

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