On a school's Annual Day, sweets were to be distributed equally among 112 children. However, 32 children were absent on that day, so the remaining children each received 6 extra sweets. How many sweets was each child originally supposed to get?

Introduction / Context:
This is a straightforward average and total quantity problem often seen in school level aptitude tests. Sweets are to be shared equally, but because some children are absent, the remaining children each receive more than planned. The main idea is to recognise that the total number of sweets remains the same, and the change in the number of children changes the per child share.

Given Data / Assumptions:

• Total number of children planned to receive sweets = 112.
• Number of children absent on the day = 32.
• Number of children actually present = 112 - 32 = 80.
• Each present child receives 6 sweets more than originally planned.
• Total number of sweets remains fixed and is fully distributed among the present children.
• We must find the original number of sweets per child.

Concept / Approach:
Let the original number of sweets intended for each child be s. Then the total number of sweets is 112s. When only 80 children are present, these same 112s sweets are distributed equally, and each of the 80 children now receives s + 6 sweets. Therefore, the new distribution gives 80(s + 6) sweets in total. Since the total number of sweets has not changed, we can set 112s equal to 80(s + 6) and solve for s.

Step-by-Step Solution:
Step 1: Let s be the original number of sweets for each child. Step 2: Total sweets purchased or prepared = 112s. Step 3: Number of children present = 112 - 32 = 80. Step 4: Each present child now receives s + 6 sweets. Step 5: Total sweets distributed among present children = 80(s + 6). Step 6: Equate the totals: 112s = 80(s + 6). Step 7: Expand the right side: 112s = 80s + 480. Step 8: Subtract 80s from both sides: 32s = 480. Step 9: Divide both sides by 32: s = 480 / 32 = 15. Step 10: Therefore, each child was originally supposed to receive 15 sweets.

Verification / Alternative check:
Check with the computed value s = 15. Total sweets = 112 * 15 = 1680. If all 112 children had been present, each would have got 15 sweets. With only 80 present, each gets 15 + 6 = 21 sweets, for a total of 80 * 21 = 1680 sweets, which matches the original total. This confirms that the calculation is correct.

Why Other Options Are Wrong:
If each child originally received 14 sweets, total sweets would be 112 * 14 = 1568, and then each of the 80 present children would get 19.6 sweets, which is not a whole number. Other values like 16, 12 or 18 similarly fail to give both an integer increase of 6 sweets per child and equal distribution using whole numbers of sweets. Only 15 satisfies all the constraints nicely.

Common Pitfalls:
One common mistake is to try to guess the number of sweets per child without setting up the equation. Another is to confuse the number of absent children with the number of present children when writing the total distribution. Some students also mistakenly think that 6 extra sweets per child translates directly to 6 fewer children, which is not always correct. Systematically writing the equation based on fixed total sweets avoids such errors.

Final Answer:
Each child was originally supposed to get 15 sweets.