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A boatman takes his boat in a river against the stream from a place A to a place B where AB is 21 km and again returns to A. Thus he takes 10 hours in all. The time taken by him downstream in going 7 km is equal to the time taken by him against stream in going 3 km. Find the speed of river.
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- 2 kmph
- 2.5 kmph
- 3 kmph
- 3.5 kmph
Correct Option: A
Let the speed of boat and river be x km per hr. and y km per hr. respectively.
Then, The speed of boatman downstream = (x + y) km per hr.
and the speed of boatman upstream = (x – y) km per hr.
Time taken by boatman in going 21 km downstream
| = | hours | |
| x + y |
Time taken by boatman in going 21 km upstream
| = | hrs. | |
| x − y |
According to the question,
| = | = | = 10 ...(i) | ||
| x + y | x − y |
| Now, time taken for 7 kms downstream = | hrs. | |
| x + y |
| and time taken for 3 kms upstream = | hrs. | |
| x − y |
According to the question
| − | = 0 ...(ii) | ||
| x + y | x − y |
By (ii) × 7 + (i)
| − | = | = | = 10 | ||||
| x + y | x − y | x + y | x − y |
| ⇒ | = 10 | |
| x + y |
⇒ x + y = 7 ...(iii)
Putting x + y = 7 in equation (ii)
we have
| − | = 0 | ||
| 7 | x − y |
| ⇒ 1 − | = 0 | |
| x − y |
⇒ x – y = 3 ...(iv)
On adding (iii) and (iv), we have
2x = 10
⇒ x = 5
∴ y = 7 – x = 7 – 5 = 2
∴ Speed of river = 2 km per hr.
