Question

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

• A. If the data in statement (1) alone is sufficient to answer the question
• B. If the data in statement (2) alone is sufficient to answer the question
• C. If the data in both the statements together are needed to answer the question
• D. If either statement (1) alone or statement (2) alone is sufficient to answer the question

Hint:

Speed needs a revolutions-per-time rate, not just a revolutions-to-diameter ratio with no time attached.

Answer 1

The Correct Option is B

Step 1: Work out what is actually needed.
Speed of the wheel = (distance covered per revolution) x (number of revolutions per unit time).
The diameter is already known (70 cm), so the circumference, \(\pi \times 70\) cm, can always be found. What is missing is the number of revolutions per unit of time (a rate), not just a raw revolution count.

Step 2: Check statement 1 alone.
Statement 1 says the ratio of revolutions to diameter is 2:3, which only compares a number of revolutions to the diameter value, with no mention of how much time those revolutions take.
Without a time reference, this ratio cannot be converted into a speed.
So statement 1 alone is not sufficient.

Step 3: Check statement 2 alone.
Statement 2 says the wheel makes 40 revolutions every 10 seconds, which is 4 revolutions per second, a genuine rate.
The distance covered per revolution is the circumference, \(\pi \times 70 \approx 219.8\) cm.
So the speed is \(4 \times 219.8 = 879.2\) cm per second, which converts to kmph as \(879.2 \times 36/1000 \approx 31.65\) kmph. This is one clear numeric answer, so statement 2 alone is sufficient.

Final Answer:
Statement 2 alone supplies the missing rate and lets us compute a definite speed, while statement 1 alone cannot, since it never gives a time base. \[ \boxed{\text{b - Statement (2) alone is sufficient}} \]