Question

Mohan can reach his destination on time by travelling at a speed of 54 km/hr. If one-fourth of the time, he covers \( \frac{2}{9} \) of the total distance, at what speed should the remaining distance be travelled so as to reach his destination on time?

• A. 60 km/hr
• B. 58 km/hr
• C. 56 km/hr
• D. 54 km/hr

Hint:

When a question involves time and fractional distance, assume a total distance that's a multiple of denominators to simplify calculations.

Answer 1

The Correct Option is C

Let total distance = 108 km (LCM of 9 and 12 for easier calculation).
\[ \text{Given speed} = 54 \text{ km/hr} \quad \Rightarrow \quad \text{Total time} = \frac{108}{54} = 2 \text{ hours} \] Step 1: In \( \frac{1}{4} \) of the time i.e. \( \frac{1}{2} \) hour, distance covered = \( \frac{2}{9} \times 108 = 24 \) km Step 2: Remaining distance = \( 108 - 24 = 84 \) km
Remaining time = \( 2 - \frac{1}{2} = \frac{3}{2} \) hours Step 3: Required speed = \( \frac{84}{3/2} = \frac{84 \times 2}{3} = 56 \) km/hr