If the total price of 23 toys is Rs 276, then what will be the total price of 12 such toys bought at the same rate?

Introduction / Context:
This question is a basic application of the unitary method and direct proportion in arithmetic. The idea is that if the cost of a certain number of toys is known, then the cost of any other number of the same toys at the same rate can be found by first finding the cost of one toy and then scaling up or down. Such questions are very common in aptitude tests because they check a candidate's understanding of proportional reasoning and careful calculation.

Given Data / Assumptions:

• The total price of 23 toys is Rs 276.
• All toys are identical and are sold at the same constant rate.
• We need to find the price of 12 toys at this same rate.
• There are no discounts or extra charges involved.

Concept / Approach:
The concept used is direct proportion and the unitary method. When the price is directly proportional to the number of items, we can write: price per toy = total price / number of toys Once the price of one toy is known, the price of any other number of toys is: price of required toys = price per toy * number of required toys All calculations are done with simple division and multiplication.

Step-by-Step Solution:
Step 1: Total price of 23 toys = Rs 276. Step 2: Find the price of one toy using unitary method. price per toy = 276 / 23 276 divided by 23 is 12, so price per toy = Rs 12. Step 3: Now we need the price of 12 toys. price of 12 toys = price per toy * 12 price of 12 toys = 12 * 12 = 144 So the required cost of 12 toys is Rs 144.

Verification / Alternative check:
We can verify quickly. If one toy costs Rs 12, then 23 toys should cost: 23 * 12 = 276 This matches the given total price, so our price per toy is correct. Scaling from 23 to 12 toys is also consistent because the relation between quantity and cost is linear for a constant rate.

Why Other Options Are Wrong:
Option b (148): This would imply a non integer or incorrect price per toy and does not match the original total of Rs 276 for 23 toys.
Option c (156): This would correspond to a higher unit price and would not give 276 when multiplied back by 23.
Option d (186): This is much larger than the correct value and clearly does not fit the proportional relationship.

Common Pitfalls:
Students sometimes directly try to form a shortcut without first finding the price per toy, which can cause errors. Another common mistake is doing 23 * 12 instead of 276 / 23, or mis dividing 276 by 23. Careless multiplication, such as computing 12 * 12 incorrectly, may also lead to wrong answers in an otherwise simple question. Always ensure that the unit price is found correctly before scaling up or down.

Final Answer:
The total price of 12 toys at the same rate is Rs 144.