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A 91 cm long copper wire is cut into two pieces whose lengths are in the ratio 6 : 7. Find the length of the SHORTER piece.

Class 6Ratio and ProportionRatio and Proportion
  • A49 cm
  • B45.5 cm
  • C39 cm
  • D42 cm

Step-by-Step Solution

Total parts = 6 + 7 = 13, so one part = 91 ÷ 13 = 7 cm. The shorter piece has 6 parts = cm (the longer piece is cm). Picking 49 cm gives the longer piece, and 45.5 cm is half of 91 — that would be a 1 : 1 cut, not 6 : 7.
Answer: D) 42 cm

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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