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A man covered a certain distance at some speed. Had he moved 3 km per hour faster, he would have taken 40 minutes less. If he had moved 2 km per hour slower, he would have taken 40 minutes more. The distance (in km) is :
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- 20
- 35
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36 2 3 - 40
Correct Option: D
Let the distance be x km and initial speed be y kmph.
According to question,
| − | = | ...(i) | |||
| y | y + 3 | 60 |
and,
| − | = | ...(ii) | |||
| y − 2 | y | 60 |
From equations (i) and (ii),
| − | = | = | ||||
| y | y + 3 | y − 2 | y |
| ⇒ | − | = | = | ||||
| y | y + 3 | y − 2 | y |
| ⇒ | = | ||
| y(y + 3) | y(y − 2) |
⇒ 3 (y – 2) = 2 (y + 3)
⇒ 3y – 6 = 2y + 6
⇒ y = 12
From equation (i),
| ⇒ | − | = | ⇒ | = | |||||
| 12 | 15 | 60 | 60 | 3 |
| ⇒ x = | × 60 = 40 | |
| 3 |
∴ Distance = 40 km.
