Question

The speeds of two trains are in the ratio 6:7. If the second train runs 364 km in 4 hours, then the speed of the first train is

• A. 60 km/hr
• B. 72 km/hr
• C. 78 km/hr
• D. 84 km/hr

Answer 1

The Correct Option is C

Finding the Speed of the First Train 

Step 1: Define Variables

Let the speeds of the two trains be:

• First train: \( 6x \) km/hr
• Second train: \( 7x \) km/hr

Step 2: Compute the Speed of the Second Train

We are given that the second train covers 364 km in 4 hours. Using the speed formula:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Substituting values:

\[ 7x = \frac{364}{4} = 91 \text{ km/hr} \]

Step 3: Solve for \( x \)

\[ x = \frac{91}{7} = 13 \]

Step 4: Compute the Speed of the First Train

\[ 6x = 6 \times 13 = 78 \text{ km/hr} \]

Final Answer:

Thus, the speed of the first train is 78 km/hr (Option C).