The mean of seven numbers is 96. If an eighth number is added, the mean becomes 112. Find the eighth number.

Analyze the question: We're given the mean of 7 numbers and the new mean after an 8th number is added. We need to find that 8th number.

Concept: Mean = (Sum of numbers) ÷ (Number of numbers), so Sum = Mean × Number of numbers.

Solution:

1. Sum of the first 7 numbers = 96 × 7 = 672
2. Sum of all 8 numbers = 112 × 8 = 896
3. Eighth number = 896 − 672 = 224

Check: (672 + 224) ÷ 8 = 896 ÷ 8 = 112 ✓

Answer: Option D (224).

Tip: For "a new number is added" mean questions, always convert each mean back to a total (mean × count), then subtract the old total from the new total. A quick shortcut: the new number = new mean + (old count × change in mean) = 112 + 7 × 16 = 224.