Question

Malya and Malaraj start jogging together in the same direction to cover a certain distance. Mallya runs at the speed of 4 km/hr and Malaraj at 2 km/hr. If Mallya arrives 15 minutes before Malaraj, then what is the distance covered by each of them?

• A. 7.5 kms
• B. 3 kms
• C. 2 kms
• D. 1 kms

Answer 1

The Correct Option is D

Finding the Distance Covered by Mallya and Malaraj

Given Data:

• Speed of Mallya = 4 km/hr 
• Speed of Malaraj = 2 km/hr
• Mallya arrives 15 minutes before Malaraj

Step 1: Express Time Taken by Each Person

Let the distance covered by each of them be \( d \) km.

• Time taken by Mallya: \[ \frac{d}{4} \]
• Time taken by Malaraj: \[ \frac{d}{2} \]

Step 2: Set Up the Time Difference Equation

We are given that Mallya arrives 15 minutes before Malaraj. Converting 15 minutes into hours:

\[ 15 \text{ minutes} = \frac{15}{60} = \frac{1}{4} \text{ hours} \]

Thus, the equation becomes:

\[ \frac{d}{2} - \frac{d}{4} = \frac{1}{4} \]

Step 3: Solve for \( d \)

Rewriting the equation:

\[ \frac{2d}{4} - \frac{d}{4} = \frac{1}{4} \]

\[ \frac{d}{4} = \frac{1}{4} \]

Multiplying both sides by 4:

\[ d = 1 \]

Final Answer:

Thus, the distance covered by each of them is 1 km. The correct answer is (D) 1 km.