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A person can row a boat 32 km upstream and 60 km downstream in 9 hours. Also, he can row 40 km upstream and 84 km downstream in 12 hours. Find the rate of the current.
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- 3 kmph
- 2.5 kmph
- 1.5 kmph
- 2 kmph
Correct Option: D
Let the upstream speed be x km per hr. and downstream speed be y km per hr.
Then, we can write,
| + | = 9 | ||
| x | y |
| and, | + | = 12 | ||
| x | y |
| Let | = m and | = n | ||
| x | y |
The above two equations can now be written as
32 m + 60 n = 9 ...(i)
and, 40 m + 84 n = 12 ...(ii)
7 × (i) – 5 × (ii) gives 24 m = 3
| or m = | or x = 8 km per hr. | |
| 8 |
4 × (ii) – 5 × (i) gives 36 n = 3
| or n = | or y = 12 km per hr. | |
| 12 |
Rate of current
| = | = | = 2 km. per hr. | ||
| 2 | 2 |
