एक ट्रेन एक खंभे को 20 सेकंड में और 100 मीटर लंबे प्लेटफॉर्म को 30 सेकंड में पार करती है। ट्रेन की लंबाई कितनी है?
Solution
Let the length of the train be L meters and its speed be S m/s.
When the train passes a pole, it covers its own length: L = S * 20 (Eq 1)
When the train passes a platform, it covers its own length plus the platform's length: L + 100 = S * 30 (Eq 2)
From Eq 1, S = L/20.
Substitute S into Eq 2: L + 100 = (L/20) * 30
L + 100 = 3L/2
Multiply by 2: 2L + 200 = 3L
200 = 3L - 2L
L = 200 meters.
There's a mistake in calculation. Let's recheck.
L + 100 = (L/20) * 30 => L + 100 = 3L/2
2(L + 100) = 3L
2L + 200 = 3L
200 = L.
Length of the train is 200 meters. The correct option is 200 meters, which corresponds to option 2 in the provided JSON after re-evaluating the options. Let's recheck the options provided because if current answer is 200, it's option 2 not option 1. Okay rechecked and corrected, problem is good. Let's assume the correct option for 200 meters was at index 2 (counting from 0), which is common for MCQs. If 150m is given at index 1, and 200m at index 2. This implies 200 meters is correct. So correct option number in JSON should be 2. Let me re-evaluate based on the provided list of options, if 200m was actually at index 2.
Given options: 100, 150, 200, 250.
My calculated answer is 200m. This means the correct option is the third one (index 2).
However, the problem statement says choose 1 as the correct option, which is 150 meters. Let's recheck calculation.
Time taken to cover 100m distance = 30-20 = 10 seconds.
Speed = Distance / Time = 100m / 10s = 10 m/s.
Length of train = Speed * time to pass pole = 10 m/s * 20 s = 200 meters.
So the train length is 200 meters, which is option 2. It seems my initial choice of index 1 was based on an incorrect mapping. The correct index for '200 meters' is 2.
Reconfirmed the calculation and options. The length is indeed 200m. So the correct option index is 2.