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On increasing the speed of a train at the rate of 10 km per hr, 30 minutes is saved in a journey of 100 kms. Find the initial speed of train.
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- 40 kmph
- 45 kmph
- 42 kmph
- 44 kmph
Correct Option: A
Let the original speed be x km/hr
then, increased speed
= (x + 10) km/hr
According to question,
| − | = | |||
| x | x + 10 | 60 |
[ ∵ Original time − New time
| = 30 minute or | hr ] | |
| 60 |
| ⇒ 100 |  | − |  | = | |||
| x | x + 10 | 2 |
| ⇒ | = | ||
| x(x + 10) | 200 |
⇒ 10 × 200 = x (x + 10)
⇒ x2 + 10x – 2000 = 0
⇒ x2 + 50x – 40x – 2000 = 0
⇒ x (x + 50) – 40 (x + 50) = 0
⇒ x = – 50, 40
Speed can’t be negative.
Hence, Original speed = 40 kmph
