A box of sweets is distributed between persons A and B in the ratio 3 : 4. If A receives 36 sweets, how many sweets were there in the box in total?

Introduction / Context:
This is a basic ratio and proportion problem where the total quantity is divided between two people in a given ratio. One person share is known, and we are asked to find the total number of items. Such questions are fundamental in ratio topics and appear frequently in competitive exams and school tests.

Given Data / Assumptions:

• Sweets are divided between A and B in the ratio 3 : 4.
• A receives 36 sweets.
• We assume all sweets are counted correctly and there is no wastage.
• We are asked to find the total number of sweets in the box.

Concept / Approach:
If two quantities are in ratio a : b, they can be represented as a * k and b * k for some common multiplier k. Here A share corresponds to 3 parts and B share to 4 parts. Since A share is known numerically, we can find k by dividing that share by the number of ratio parts associated with A. Once k is known, the total is (3k + 4k) = 7k.

Step-by-Step Solution:
Let A share = 3k and B share = 4k for some positive k. Given that A receives 36 sweets, we have 3k = 36. So k = 36 / 3 = 12. Total sweets = 3k + 4k = 7k. Substitute k = 12: total sweets = 7 * 12 = 84. Therefore, the box contained 84 sweets.

Verification / Alternative check:
Using the total 84 sweets, A share should be (3 / 7) of 84 and B share should be (4 / 7) of 84. Compute (3 / 7) * 84 = 36, which matches the given amount for A. B share is (4 / 7) * 84 = 48. Therefore the distribution 36 and 48 is in ratio 3 : 4 and sums to 84, confirming the correctness of the total.

Why Other Options Are Wrong:
12 is only part of A share and is far less than the required total. 144 and 27 do not produce a share of exactly 36 for A when the ratio 3 : 4 is applied. 63 would give A share (3 / 7) * 63 = 27, not 36, so it does not satisfy the condition.

Common Pitfalls:
A common error is to divide 36 by 4 instead of 3, or to use 3 + 4 = 7 incorrectly. Another mistake is to assume that 36 is the total and then try to split it in ratio 3 : 4, which is not what the problem states. Carefully identifying which person share is given and which ratio part belongs to that person is essential for solving these problems correctly.

Final Answer:
The total number of sweets in the box is 84.