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A motorist and a cyclist start from A to B at the same time. AB is 18 km. The speed of motorist is 15 m per hr. more than the cyclist. After covering half the distance, the motorist rests for 30 minutes and thereafter his speed is reduced by 20%. If the motorist reaches the destination B, 15 minutes earlier than that of the cyclist, then find the speed of the cyclist.
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- 16 kmph
- 12 kmph
- 14 kmph
- 15 kmph
Correct Option: B
Let the speed of the cyclist be x km per hr.
Speed of the motorist= (x + 15) km per hr.
Time taken by the motorist to cover half of the distance
| = | = | hrs. | ||
| 2 × (x + 15) | x + 15 |
After covering 9 kms, the speed of motorist gets reduced by 20%
| ∴ New speed = (x + 15) × | |
| 100 |
| = | km per hr. | |
| 5 |
Time taken by the motorist to cover the remaining half distance
| = | = | hrs. | ||
| 4 (x + 15) | 4 (x + 15) |
Total time taken by the motorist
| = | + | + | hrs. | |||
| x + 15 | 2 | 4 (x + 15) |
| Total time taken by the cyclist = | hrs. | |
| x |
| Motorist reaches 15 minutes, i.e., | hr. earlier. | |
| 4 |
| ∴ | − | − | − | = | |||||
| x | x + 15 | 2 | 4 (x + 15) | 4 |
| ⇒ | = | ||
| 4x (x + 15) | 4 |
⇒ 72x + 1080 – 36x – 2x2 – 30x – 45x = x2 + 15
⇒ 3x2 + 54x – 1080 = 0
⇒ x2 + 18x – 360 = 0
⇒ x2 + 30x – 12x – 360 = 0
⇒ x (x + 30) – 12 (x + 30) = 0
⇒ (x + 30) (x – 12) = 0
⇒ x = – 30, 12
The speed cannot be negative.
∴ The speed of the cyclist = 12 km per hr.
