Q) A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.

(Q 36 – 30/1/3 – CBSE 2026 Question Paper)

Ans: 

Step 1: Let’s consider the speed of faster train is = X km/ hr

∴ the speed if slower train is = (X – 10) km/hr

Step 2: ∴ Time taken by faster train = hrs

and Time taken by slower train = hrs

Step 3: Time by slower train – Time by faster train = 1     [given]

∴ = 1

∴ = 1

∴ 200 X – 200 (X – 10) =  X (X -10)

∴ 200 X – 200 X + 2000 =  X² – 10 X

∴ X² – 10 X – 2000 = 0

∴ X² – 50 X + 40 X – 2000 = 0

∴ X (X – 50) + 40 (X – 50) = 0

∴ (X – 50) (X + 40) = 0

∴ X = 50 or X = – 40

Here, we reject X = – 40 because speed can not have negative value.

∴ X = 50

∴ Speed of faster train is 50 km/hr

and Speed of slower train is 50 – 10 = 40 km/hr.

Therefore, the speeds of faster & slower trains are 50 km/hr and 40 km/hr respectively.

Check:
Time taken by slower train= = 5 hrs
Time taken by faster train = = 4 hrs
Time difference = 5 – 4 = 1 hr
Since it matches with the given condition on the question, hence our solution is correct.

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