Correct Answer: 3 : 2
Explanation:
Step 1: Let the lengths of the two trains be L₁ and L₂, and their speeds be S₁ and S₂.
Step 2: The two trains cross each other in 23 seconds when moving in opposite directions.
That means:
L₁ + L₂ = (S₁ + S₂) × 23
Step 3: Substitute L₁ and L₂
S₁ × 27 + S₂ × 17 = (S₁ + S₂) × 23
Step 4: Expand and simplify the equation
27S₁ + 17S₂ = 23S₁ + 23S₂ => 27S₁ - 23S₁ = 23S₂ - 17S₂ => 4S₁ = 6S₂ => S₁ / S₂ = 6 / 4 = 3 / 2
Answer: 3 : 2
The ratio of their speeds is 3:2.
This is a classic relative motion problem involving trains. It uses the concept of time = distance/speed, and setting up linear equations from the conditions provided. This type of question is commonly asked in competitive exams like SSC, Railway, and Banking.
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