Average, Mixture and Alligation Question 1 - CAT 2021
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:
Step-by-Step Explanation
Let the fixed amount spent in each of the first three months be Rs. 100. The amount spent in each of the next two months is half of that, which equals Rs. 50.
- Calculate the total expense:
Total Expense = 100 + 100 + 100 + 50 + 50 = Rs. 400
- Calculate the total quantity bought:
- Month 1 (at Rs. 10/kg): 100 / 10 = 10 kg
- Month 2 (at Rs. 20/kg): 100 / 20 = 5 kg
- Month 3 (at Rs. 25/kg): 100 / 25 = 4 kg
- Month 4 (at Rs. 25/kg): 50 / 25 = 2 kg
- Month 5 (at Rs. 50/kg): 50 / 50 = 1 kg
Total Quantity = 10 + 5 + 4 + 2 + 1 = 22 kg
- Calculate the average price per kg:
Average Price = 400 / 22 ≈ 18.18
The closest integer value is 18.
Correct Option: B
💡 FundaMakers Tip:
When a problem deals with weighted averages where the price changes but absolute expenditure remains locked in an easy ratio, assume a convenient scale value (like Rs. 100). This transforms complex variable weight formulas into simple integer division steps, ensuring quick computation.