Question

Two trains running in the same direction on two parallel tracks take 30 seconds and 60 seconds to cross a stationary pole. If the faster train takes 50 seconds to overtake the slower train completely, then what is the ratio of the speed of the faster to the slower train?

• A. 11:2
• B. 9:2
• C. 7:2
• D. 5:2

Answer 1

The Correct Option is A

Step 1: Define Variables 

• Let the length of the slower train be L₁ and its speed be S₁.
• Let the length of the faster train be L₂ and its speed be S₂.

Step 2: Use the Formula for Time Taken to Cross a Stationary Pole

The formula for time taken to cross a stationary pole is:

Time = \( \frac{\text{Length}}{\text{Speed}} \).

From the given information:

\( \frac{L_1}{S_1} = 60 \) and \( \frac{L_2}{S_2} = 30 \).

Step 3: Use the Formula for Time Taken to Overtake

The formula for time taken for one train to overtake another is:

Time = \( \frac{L_1 + L_2}{S_2 - S_1} \).

Given that the faster train takes 50 seconds to overtake the slower train:

\( \frac{L_1 + L_2}{S_2 - S_1} = 50 \).

Step 4: Express Lengths in Terms of Speed

Using the given data:

\( L_1 = 60S_1 \), \( L_2 = 30S_2 \).

Substituting into the equation:

\( \frac{60S_1 + 30S_2}{S_2 - S_1} = 50 \).

Multiplying both sides by \( S_2 - S_1 \):

\( 60S_1 + 30S_2 = 50(S_2 - S_1) \).

Expanding and rearranging:

\( 60S_1 + 30S_2 = 50S_2 - 50S_1 \).

\( 110S_1 = 20S_2 \).

\( \frac{S_2}{S_1} = \frac{110}{20} = \frac{11}{2} \).

Final Conclusion

The ratio of the speed of the faster train to the slower train is 11:2, so the correct answer is (A) 11:2.