If each child is given 10 sweets, there are 3 sweets left over. But if each is given 11, then the number of sweets is 4 less. Fin…

Question

If each child is given 10 sweets, there are 3 sweets left over. But if each is given 11, then the number of sweets is 4 less. Find the number of sweets.

1. A. 37
2. B. 57
3. C. 73 (Correct answer)
4. D. 75

Correct Answer

Option C — 73

Detailed Solution & Explanation

The correct answer is 73.

Key Points

• Let the number of children be n and sweets be S.
• Giving 10 each leaves 3 over: S = 10n + 3.
• Giving 11 each falls short by 4: S = 11n − 4.
• Equating: 10n + 3 = 11n − 4, so n = 7.
• Therefore S = 10(7) + 3 = 73 sweets.

Additional Information

• The key is translating the two conditions into equations of the same quantity:
  • "3 left over" means the total exceeds an exact share: S = 10n + 3
  • "4 less" means the total falls short of an exact share: S = 11n − 4
• Watch the sign convention closely — reading "4 less" as *+4* is the single most common error in this question type.
• Substituting back is a quick check: with 7 children, 10 each uses 70 and leaves 3; 11 each would need 77, which is 4 more than the 73 available.