DSSSB TGT CS 2023 Shift 2 – Question 053

A 240-m-long train passes a pole in 18 seconds and completely passes another train running in the opposite direction at a speed of 42 km/h in 17 seconds. What is the length of the other train?

• 170 m
• 185 m
• 195 m
• 200 m

Step 1: Calculate the speed of the first train:
Length of first train \(L_1 = 240\text{ m}\).
Time to pass a pole = 18 s.
\[ v_1 = \frac{L_1}{t} = \frac{240}{18} = \frac{40}{3}\text{ m/s} \]

Step 2: Convert the speed of the second train to m/s:
Speed of second train \(v_2 = 42\text{ km/h}\).
\[ v_2 = 42 \times \frac{5}{18} = \frac{7 \times 5}{3} = \frac{35}{3}\text{ m/s} \]

Step 3: Calculate the relative speed:
Since the two trains run in opposite directions, their relative speed is the sum of their individual speeds:
\[ v_{\text{rel}} = v_1 + v_2 = \frac{40}{3} + \frac{35}{3} = \frac{75}{3} = 25\text{ m/s} \]

Step 4: Find the length of the second train \(L_2\):
Total distance covered when passing each other is \(L_1 + L_2\):
\[ L_1 + L_2 = v_{\text{rel}} \times t = 25 \times 17 = 425\text{ m} \]
Given \(L_1 = 240\text{ m}\):
\[ L_2 = 425 – 240 = 185\text{ m} \]
Hence, the length of the other train is 185 m and the correct answer is option b).