Question:
Two trains 'A' and 'B' started running at the same time. Train 'A' takes 3 hours more than train 'B' to cover 540 km. But if train 'A' doubles its speed, it covers 540 km in 1½ hours less than train 'B'. What is the speed (in km/h) of train 'B'?
Two trains 'A' and 'B' started running at the same time. Train 'A' takes 3 hours more than train 'B' to cover 540 km. But if train 'A' doubles its speed, it covers 540 km in 1½ hours less than train 'B'. What is the speed (in km/h) of train 'B'?
Updated On: Sep 16, 2026
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The Correct Option is B
Solution and Explanation
Concept:
Step 1: Set up train B's time and train A's time
Let train B take t hours to cover 540 km, so speed of B = 540/t.
Train A takes 3 hours more than B, so A's time = t + 3, and A's speed = 540/(t + 3).
Step 2: Use the condition when train A doubles its speed
New speed of A = 2 x 540/(t + 3) = 1080/(t + 3)
New time of A = 540 ÷ [1080/(t + 3)] = 540(t + 3)/1080 = (t + 3)/2
Step 3: Use the given condition that this new time is 1.5 hours less than B's time
(t + 3)/2 = t - 1.5
Multiply both sides by 2: t + 3 = 2t - 3
3 + 3 = 2t - t
t = 6
Step 4: Find the speed of train B
Speed of B = 540/t = 540/6 = 90 km/hr
Final Answer: 90 km/hr
- For the same distance, if speed doubles, the time taken becomes exactly half the original time.
- Write time = distance/speed for each train and use the given time differences to form equations.
- Solve the resulting linear equation for the unknown time, then find the required speed.
Step 1: Set up train B's time and train A's time
Let train B take t hours to cover 540 km, so speed of B = 540/t.
Train A takes 3 hours more than B, so A's time = t + 3, and A's speed = 540/(t + 3).
Step 2: Use the condition when train A doubles its speed
New speed of A = 2 x 540/(t + 3) = 1080/(t + 3)
New time of A = 540 ÷ [1080/(t + 3)] = 540(t + 3)/1080 = (t + 3)/2
Step 3: Use the given condition that this new time is 1.5 hours less than B's time
(t + 3)/2 = t - 1.5
Multiply both sides by 2: t + 3 = 2t - 3
3 + 3 = 2t - t
t = 6
Step 4: Find the speed of train B
Speed of B = 540/t = 540/6 = 90 km/hr
Final Answer: 90 km/hr
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