Question

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

• A. 18
• B. 26
• C. 16
• D. 20

Answer 1

The Correct Option is A

Suppose the family allocates Rs. 100 per month for the initial three months, followed by Rs. 50 per month for the subsequent two months. This results in them purchasing 10, 5, 4, 2, and 1 kilograms of onions during the first five months, respectively. In total, they acquire 22 kilograms of onions. Their total expenditure over these five months amounts to Rs. 400.

Step 1: Calculating the Average Cost per Kilogram

The average cost per kilogram of onions is given by the formula: \[ \text{Average Expense} = \frac{\text{Total Expenditure}}{\text{Total Amount Bought}} \] Substituting the given values: \[ \text{Average Expense} = \frac{400}{22} \approx 18 \, \text{rupees per kilogram}. \]

Final Answer:

The average cost per kilogram is Rs. \( \boxed{18} \).

Answer 2

Given: Onions were sold at the following prices over the past five months:

Month	Price per kg (Rs)	Amount Spent (Rs)	Quantity Purchased (kg)
1	10	100	\( \frac{100}{10} = 10 \)
2	20	100	\( \frac{100}{20} = 5 \)
3	25	100	\( \frac{100}{25} = 4 \)
4	25	50	\( \frac{50}{25} = 2 \)
5	50	50	\( \frac{50}{50} = 1 \)

🔍 Step-by-Step Calculation

• Total amount spent over 5 months: \( 100 + 100 + 100 + 50 + 50 = 400 \) Rs
• Total quantity of onions purchased: \( 10 + 5 + 4 + 2 + 1 = 22 \) kg

💡 Average cost per kg:

\[ \text{Average Cost per kg} = \frac{\text{Total Amount Spent}}{\text{Total Quantity}} = \frac{400}{22} \approx \boxed{18.18} \text{ Rs/kg} \]

✅ Final Answer: ₹18.18 per kg

This average is weighted by quantity, not by simple price average, which reflects the real cost per kilogram of onions purchased over time.