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A hockey team played 30 matches and won 18 of them, losing the rest. The ratio of matches won to matches lost is 3 : 2. What is the ratio of matches won to matches PLAYED?

Class 6Ratio and ProportionRatio and Proportion
  • A3 : 5
  • B3 : 2
  • C2 : 5
  • D5 : 3

Step-by-Step Solution

Matches played = 30 and matches won = 18, so won : played = 18 : 30 = 3 : 5. Repeating 3 : 2 is the trap — that is won : lost, a part-to-part ratio. Here the second quantity is the total, so the part-to-whole ratio 3 : 5 is needed. 2 : 5 is lost : played.
Answer: A) 3 : 5

Key idea: What a ratio means

The ratio 2 : 3 says: for every 2 of one thing, there are 3 of another. In a fruit basket of 2 apples and 3 oranges, the ratio of apples to oranges is 2 : 3. **Order matters** — the ratio of oranges to apples in the same basket is 3 : 2. The two quantities must be in the same unit (you can't ratio apples to kilograms unless you convert).

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