If 3 boys shared x oranges among themselves in the ratio 3:5:8, and smallest share was 45 oranges, find the value of x

Analyze the question: Three boys share x oranges in the ratio 3:5:8. The smallest share (the "3" part) is 45 oranges. We need the total, x.

Concept: In a ratio-sharing problem, each share = (ratio part ÷ total parts) × total. Equivalently, find the value of one ratio part, then multiply by the total number of parts.

Solution:

1. Total parts = 3 + 5 + 8 = 16
2. The smallest share corresponds to 3 parts: 3 parts = 45 1 part = 45 ÷ 3 = 15
3. Total oranges: x = 16 × 15 = 240

Check:

• Shares: 3 × 15 = 45, 5 × 15 = 75, 8 × 15 = 120
• Sum: 45 + 75 + 120 = 240 ✓

Answer: x = 240, which is option E.

Tip: In ratio questions, first find the value of one part, then multiply by the total number of parts. Always add up the ratio parts first, and check by summing the shares to confirm the total.