Question
If the speed of a train is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the train.
Answer: Option A
:
A
Let the speed of the train be x km/hr.
Time=DistanceSpeed
∴ Time taken to cover 1200 km = 1200x
Reduced speed = (x−40) km/hr
∴ Time taken to cover 1200 km in reduced speed = 1200x−40
Relation between the time taken to cover 1200 km with speed x and with speed (x - 40) km/hr is as given below
1200x−40−1200x = 13 (∵20 minutes=13 hours)
⇒ 48000x(x−40) = 13
⇒ 144000=x2−40x
⇒ x2−40x−144000=0
⇒ x2−400x+360x−144000=0
⇒ x(x−400)+360(x−400)=0
⇒ (x+360)(x−400)=0
⇒ x=−360 or x=400
Since speed cannot be negative, we get x = 400 km/hr.
∴ The speed of the train is 400 km/hr.
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:
A
Let the speed of the train be x km/hr.
Time=DistanceSpeed
∴ Time taken to cover 1200 km = 1200x
Reduced speed = (x−40) km/hr
∴ Time taken to cover 1200 km in reduced speed = 1200x−40
Relation between the time taken to cover 1200 km with speed x and with speed (x - 40) km/hr is as given below
1200x−40−1200x = 13 (∵20 minutes=13 hours)
⇒ 48000x(x−40) = 13
⇒ 144000=x2−40x
⇒ x2−40x−144000=0
⇒ x2−400x+360x−144000=0
⇒ x(x−400)+360(x−400)=0
⇒ (x+360)(x−400)=0
⇒ x=−360 or x=400
Since speed cannot be negative, we get x = 400 km/hr.
∴ The speed of the train is 400 km/hr.
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