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A man walks a distance of 35 kms. He walks for some time at 4 km per hour and for some time at 5 km per hr. If he walks at 5 km per hr. instead of 4 km per hr. and 4 km per hr. instead of 5 km per hr, he will walk 2 kms more in the same span of time. Find his total time of total journey.
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- 8.5 hours
- 7.5 hours
- 8 hours
- 7 hours
Correct Option: C
Let the man walks for x hours at 4 km per hr. and y hours at 5 km per hr. and covers a distance of 35 kms.
∴ Distance = 4x + 5y = 35 ...(i)
Now, he walks at 5 km per hr.
for x hours and at 4 km per hr.
for y hours and covers a distance (35 + 2) = 37 kms
∴ Distance = 5x + 4y = 37...(ii)
By 5 × (i) – 4 × (ii) we have
| 20x + 25y = 175 |
| 20x + 16y = 148 |
| - - - |
| ____________ |
| 9y = 27 |
⇒ y = 3
Putting the value of (y) in equation (i), we have
4x + 5 × 3 = 35
⇒ 4x = 35 – 15 = 20
⇒ x = 5
∴ Total time taken
= x + y = 5 + 3 = 8 hours.
