Problems on Boats Stream
Q31. The current of a stream runs at 4 km an hour. A boat goes 6 km and back to the starting point in 2 hours. The speed of the boat in still water is
(a) 7 km/h
(b) 8 km/h
(c) 9 km/h
(d) 12 km/h
Answer: (b) 8 km/h
Let the speed in still water be x km/h
∴ Speed downstream = (x + 4) km/h
Speed upstream = (x - 4) km/h
| A/Q | 6 | + | 6 | = 2 |
| x + 4 | x - 4 |
| ⇒ | 1 | + | 1 | = 2/6 = 1/3 |
| x + 4 | x - 4 |
| ⇒ | x - 4 + x + 4 | = | 1 |
| (x + 4)(x - 4) | 3 |
| ⇒ | 2x | = | 1 |
| x2 - 16 | 3 |
⇒ x2 - 16 - 2x = 0
⇒ (x-8)(x+2) = 0
∴ x = 8 or x = -2
∴ Speed of the boat in still water = 8 km/h
Practice Test Exam