Question:medium

The diameter of the wheel of a motorcycle is 70 cm. What would be its speed in kmph?
Statement 1: The ratio of revolutions to diameter is 2:3
Statement 2: It makes 40 revolutions for every 10 seconds

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Speed needs a revolutions-per-time rate, not just a revolutions-to-diameter ratio with no time attached.
Updated On: Jul 21, 2026
  • If the data in statement (1) alone is sufficient to answer the question
  • If the data in statement (2) alone is sufficient to answer the question
  • If the data in both the statements together are needed to answer the question
  • If either statement (1) alone or statement (2) alone is sufficient to answer the question
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The Correct Option is B

Solution and Explanation

Step 1: Recall the wheel speed formula.
Speed = \(\pi \times \text{diameter} \times \text{revolutions per second} \times 3600/100000\) km/h (converting cm/s to km/h).
The diameter, 70 cm, is fixed by the question, so the only unknown is revolutions per second.

Step 2: Test statement 1.
"Ratio of revolutions to diameter is 2:3" mixes a count of revolutions with a length (diameter) in a ratio, but revolutions only mean something for speed once we know how long they took.
Since no duration is attached to this ratio, it cannot be turned into revolutions per second, so it cannot feed the speed formula. Statement 1 alone fails.

Step 3: Test statement 2.
"40 revolutions for every 10 seconds" converts directly to \(40/10 = 4\) revolutions per second.
Plugging into the formula: Speed = \(\pi \times 70 \times 4 \times 3600/100000\).
\(\pi \times 70 \approx 219.8\) cm per revolution, so distance per second = \(219.8 \times 4 = 879.2\) cm/s.
Convert: \(879.2\) cm/s \(\approx 31.65\) kmph. One definite value comes out.

Step 4: Conclude.
Only statement 2 gives the time-linked rate the formula needs, so statement (2) alone is sufficient. \[ \boxed{\text{b}} \]
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