Question:
A train 600 meters long is running at a speed of 90 km/hr. If it crosses a tunnel in one minute, then the length of the tunnel is:
A train 600 meters long is running at a speed of 90 km/hr. If it crosses a tunnel in one minute, then the length of the tunnel is:
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When crossing a tunnel, add the train length to the tunnel length to get total distance covered.
Updated On: Jul 15, 2026
- 500 meters
- 550 meters
- 600 meters
- 900 meters
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The Correct Option is D
Approach Solution - 1
Step 1: Convert speed to m/s:
$90 \text{ km/hr} = \dfrac{90 \times 1000}{3600} = 25$ m/s.
Step 2: In one minute (60 s), the train covers:
$25 \times 60 = 1500$ meters.
Step 3: Distance covered = length of train + length of tunnel:
$1500 = 600 + \text{tunnel length}$
$\text{Tunnel length} = 1500 - 600 = 900$ meters.
$90 \text{ km/hr} = \dfrac{90 \times 1000}{3600} = 25$ m/s.
Step 2: In one minute (60 s), the train covers:
$25 \times 60 = 1500$ meters.
Step 3: Distance covered = length of train + length of tunnel:
$1500 = 600 + \text{tunnel length}$
$\text{Tunnel length} = 1500 - 600 = 900$ meters.
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Approach Solution -2
The question gives a 600 metre train moving at 90 km/hr that crosses a tunnel in one minute, and asks for the tunnel's length. First convert the speed to metres per second: \( 90 \text{ km/hr} = \frac{90 \times 1000}{3600} = 25 \) m/s. We can then test each option by adding it to the train's length and checking whether the total distance takes exactly 60 seconds to cover at 25 m/s.
- 500 meters: Total distance \( = 600 + 500 = 1100 \) m. Time taken \( = 1100 \div 25 = 44 \) seconds, which is less than the 60 seconds given, so this option does not fit.
- 550 meters: Total distance \( = 600 + 550 = 1150 \) m. Time taken \( = 1150 \div 25 = 46 \) seconds, still short of 60 seconds, so this is ruled out too.
- 600 meters: Total distance \( = 600 + 600 = 1200 \) m. Time taken \( = 1200 \div 25 = 48 \) seconds, again less than the required 60 seconds, so this does not match either.
- 900 meters: Total distance \( = 600 + 900 = 1500 \) m. Time taken \( = 1500 \div 25 = 60 \) seconds, which matches the one minute crossing time given in the question exactly.
Testing each tunnel length against the fixed speed and train length shows that only 900 metres gives a crossing time of exactly one minute.
So the correct answer is 900 meters.
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Approach Solution -3
Another way to check this is to assume each tunnel length option is correct, work out what speed the train would need to cross the train-plus-tunnel distance in exactly one minute, and see which option's implied speed matches the 90 km/hr given in the question.
- 500 meters: Total distance to cover would be \( 600 + 500 = 1100 \) m in 60 seconds, an implied speed of \( \frac{1100}{60} \approx 18.3 \) m/s, which converts to about 66 km/hr, well below the 90 km/hr given.
- 550 meters: Total distance \( = 1150 \) m in 60 seconds gives an implied speed of about \( 19.2 \) m/s, or roughly 69 km/hr, still short of 90 km/hr.
- 600 meters: Total distance \( = 1200 \) m in 60 seconds gives an implied speed of \( 20 \) m/s, or 72 km/hr, again below the stated 90 km/hr.
- 900 meters: Total distance \( = 1500 \) m in 60 seconds gives an implied speed of \( 25 \) m/s, which converts exactly to \( 25 \times \frac{3600}{1000} = 90 \) km/hr, precisely matching the speed given in the question.
Only the 900 metre option produces an implied speed that exactly matches the train's actual given speed of 90 km/hr.
So the correct answer is 900 meters.
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