Unitary method (reverse count): If 16 dozens of bananas cost ₹ 360, how many bananas can be bought for ₹ 60?
Correct Answer: 32 bananas
Introduction / Context:We are given a total cost for a bulk quantity (in dozens) and asked how many individual items can be purchased for a smaller amount. Use the unitary method to compute the per-banana price and then scale by the available money.Given Data / Assumptions:
- 16 dozens = 16 × 12 = 192 bananas cost ₹ 360.
- Budget = ₹ 60.
- Assume a constant price per banana.
Concept / Approach:First compute the cost per banana. Then divide the budget by the per-banana price to find the count of bananas that can be bought.Step-by-Step Solution:
Total bananas = 16 × 12 = 192.Price per banana = 360 / 192 = ₹ 1.875.Bananas purchasable with ₹ 60 = 60 / 1.875 = 32.Verification / Alternative check:Proportion method: ₹ 360 buys 192 bananas. For ₹ 60 (which is 1/6 of ₹ 360), we can buy 1/6 of 192 = 32 bananas. Same result as the unit-price route.Why Other Options Are Wrong:
- 16 or 48 bananas: 16 is too few; 48 is too many for ₹ 60 at the given rate.
- 50 bananas: Not proportional to the given pricing.
Common Pitfalls:Forgetting that one dozen equals 12, or dividing 360 by 16 instead of 192. Always convert dozens to individual units before calculating unit price or quantities.
Final Answer:
32 bananas