Question

Sanchit and Archit cover a same distance at the rates of 10 km/hr and 12 km/hr respectively. What is the distance trave led when one takes 20 minutes longer than the other?

• A. 30 kms
• B. 10 kms
• C. 60 kms
• D. 20 kms

Answer 1

The Correct Option is D

Finding the Distance Travelled by Sanchit and Archit 

Step 1: Define Variables

Let the distance travelled by both Sanchit and Archit be \( D \).

The time taken by each is given by:

• Time taken by Sanchit: \[ \frac{D}{10} \]
• Time taken by Archit: \[ \frac{D}{12} \]

Step 2: Set Up the Equation

We are given that Sanchit takes 20 minutes longer than Archit:

\[ \frac{D}{10} - \frac{D}{12} = 20 \text{ minutes} \]

Since 20 minutes is \( \frac{1}{3} \) of an hour, we rewrite the equation:

\[ \frac{D}{10} - \frac{D}{12} = \frac{1}{3} \]

Step 3: Solve for \( D \)

Find the LCM of 10 and 12, which is 60:

\[ \frac{6D}{60} - \frac{5D}{60} = \frac{1}{3} \]

\[ \frac{D}{60} = \frac{1}{3} \]

Multiplying both sides by 60:

\[ D = 20 \]

Final Answer:

Thus, the distance travelled is 20 km (Option D).