Difficulty: Easy
Correct Answer: Rs.144
Explanation:
Introduction:
This is a direct proportion question in basic arithmetic. We know the total price for 23 toys, and the toys are identical. Therefore the price for any other number of toys can be found by first computing the unit price and then multiplying by the required quantity. Such questions commonly appear under the topic of ratio and proportion or unitary method.
Given Data / Assumptions:
Total price of 23 toys = Rs. 276. All 23 toys are identical and have the same price. We must find the total price of 12 toys at the same rate per toy.
Concept / Approach:
When items are sold at a constant price per unit, total cost is: total cost = number of units * cost per unit. We can find cost per unit by: cost per toy = total cost / number of toys. Then multiply this unit cost by 12 to get the price of 12 toys.
Step-by-Step Solution:
Step 1: Compute the price of one toy. cost per toy = 276 / 23. 23 * 10 = 230 and 23 * 2 = 46, so 23 * 12 = 276. Therefore, 276 / 23 = 12. So each toy costs Rs. 12. Step 2: Find the price of 12 toys. Price of 12 toys = 12 * 12. 12 * 12 = 144. Thus, the price of 12 toys is Rs. 144.
Verification / Alternative check:
We can also verify by scaling down and then up. If 23 toys cost Rs. 276, then 1 toy costs Rs. 12 as found. If we imagine 24 toys, they would cost 24 * 12 = 288, which is slightly more than 276, confirming that our per toy price is consistent with simple multiples of 23 and 12. The calculation is exact with no rounding.
Why Other Options Are Wrong:
Rs. 148 and Rs. 156 would correspond to per toy prices slightly greater than Rs. 12, which does not match the original information that 23 toys cost exactly Rs. 276. Rs. 186 would mean each toy costs more than Rs. 15 when multiplied by 12, clearly inconsistent. Rs. 132 would imply a cost per toy of Rs. 11, which would make 23 toys cost 23 * 11 = 253, not Rs. 276.
Common Pitfalls:
A frequent error is to try to scale directly from 23 to 12 without first finding the unit price, leading to complicated fractions or mistakes. Another mistake is miscalculating 276 / 23 under time pressure. Recognising that 23 * 12 equals 276 allows a quick mental calculation and avoids division errors.
Final Answer:
The total price of 12 toys at the same rate is Rs. 144.
Discussion & Comments