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, but the data in statement (2) alone is not sufficient.
• B. If the data in statement (2) alone is sufficient to answer the question, but the data in statement (1) alone is not sufficient.
• 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.
• E. If the data in neither statement (1) nor statement (2) is sufficient to answer the question, and more data is needed.

Hint:

Speed needs revolutions per unit TIME, not just a ratio to diameter; check which statement actually supplies a time reference.

Answer 1

The Correct Option is B

To find speed we need to know how many revolutions the wheel makes per unit of time and multiply that by the circumference.

Statement 1 says the ratio of revolutions to diameter is 2 : 3. This tells us that if we take some number of revolutions, they stand in a 2:3 ratio with the diameter (70 cm), so the number of revolutions would work out to (2/3) x 70 = 46.67. But this number is meaningless for speed because we are never told the time period over which these revolutions happen. Revolutions without a time frame cannot be converted into a speed. So statement 1 alone is not sufficient.

Statement 2 says the wheel makes 40 revolutions every 10 seconds, which is 4 revolutions per second. The circumference of the wheel is pi x diameter = (22/7) x 70 = 220 cm. In one second the wheel covers 4 x 220 = 880 cm, which is 8.8 m/s. Converting to km/h: 8.8 x 3.6 = 31.68 kmph. This is a complete, unique answer, so statement 2 alone is sufficient.

Since statement 2 alone answers the question but statement 1 alone does not, the correct choice is (b).