Children's Day distribution: Sweets were to be equally shared among 175 children. On the day, 35 children were absent, and each present child received 4 extra sweets. How many sweets were there in total?

Introduction / Context:This is a proportion problem with equal distribution and attendance change. The key is relating the per-child share before and after some students are absent, then solving for the total number of sweets.

Given Data / Assumptions:

• Planned recipients = 175 children.
• Actual recipients = 175 − 35 = 140 children.
• Each actual recipient gets 4 more sweets than originally planned.
• Total sweets = S (constant).

Concept / Approach:If each child originally would have got S/175 sweets, but actually got S/140, then the difference per child equals 4. Set up a simple equation and solve for S.

Step-by-Step Solution:Original per-child share = S / 175.Actual per-child share = S / 140.Difference = S/140 − S/175 = 4.Compute left side: S * (1/140 − 1/175) = S * ((175 − 140) / (140 * 175)) = S * (35 / 24500) = S / 700.So S / 700 = 4 → S = 4 * 700 = 2800.

Verification / Alternative check:Original plan: 2800 / 175 = 16 sweets per child. Actual: 2800 / 140 = 20 sweets per child. Difference = 4, matches the condition.

Why Other Options Are Wrong:

• 2400, 2480, 2520, 2680: Do not yield a per-child increase of exactly 4 when divided by 175 and 140.

Common Pitfalls:

• Reversing the subtraction (using original minus actual).
• Arithmetic errors in fraction subtraction.

Final Answer:2800