Direct proportion: pricing toys by quantity at a constant rate: If the price of 23 toys is ₹ 276 at a uniform per-toy price, what will be the total price (in rupees) of 12 toys at the same rate?

Difficulty: Easy

Correct Answer: 144

Explanation:


Introduction / Context:
This is a basic unitary-method question on per-item pricing. Knowing the cost for 23 toys, we compute the price per toy and scale to 12 toys, assuming the rate is unchanged and there are no discounts or surcharges for different quantities.


Given Data / Assumptions:

  • Total price for 23 toys = ₹276
  • Find total price for 12 toys at same per-toy price
  • Uniform pricing (linear relationship)


Concept / Approach:
Unit price = total / quantity. Multiply the unit price by the new quantity to get the new total. This is direct proportion: cost ∝ number of toys.


Step-by-Step Solution:
Per-toy price = 276 / 23 = ₹12Price for 12 toys = 12 * 12 = ₹144


Verification / Alternative check:
Ratio approach: 12/23 of ₹276 = ₹(276 * 12 / 23) = ₹(12 * 12) = ₹144, confirming the unit method.


Why Other Options Are Wrong:
158, 159, and 166 are not integer multiples of ₹12 for 12 items; 132 corresponds to 11 toys, not 12.


Common Pitfalls:
Arithmetic slips when dividing 276 by 23. Note that 23 * 12 = 276, making the unit price a neat integer here.


Final Answer:
144

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