Question

What is the speed of the car? I. The speed of a car is 10 km/hr more than that of a motorcycle.
II. The motorcycle takes 2 hr more than the car to cover 100 km.

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

When speeds are related by difference and times are related for a fixed distance, combining gives solvable equations.

Answer 1

The Correct Option is C

I alone: Only relates speeds of car and motorcycle, no absolute value. Not sufficient.
II alone: Only relates motorcycle’s speed and time difference, but car’s speed unknown. Not sufficient.
Together: Let motorcycle’s speed be $x$ km/hr. Car’s speed = $x+10$. From II: $\frac{100}{x} - \frac{100}{x+10} = 2$ gives a solvable equation for $x$ and hence the car’s speed.