The current of a stream runs at the rate of 4 k an hour A boat goes 6 km and comes back to the start...........

Quantitative Aptitude ( CCS) Boats and Streams

The current of a stream runs at the rate of 4 k an hour. A boat goes 6 km and comes back to the starting point in 2 hours. the speed (in km/ hr) of the boat in still water is

6 km/hr

8 km/hr

7.5 km/hr

6.8 km/hr

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Explanation:

Speed of the stream, y = 4 km/h
Let the speed of the boat in still water = x km/h
Downstream speed = (x + y) km/h
Upstream speed = (x + y) km/h
ATQ
6 / (x + 4) + 6 / (x - 4) = 2
Take option (b)
6 / (8 + 4) + 6 / (8 - 4) = 6/12 + 6/4
= ½ + 3/2 = 4/2 = 2
Thus, Option (b) is the answer.

Alternate:
T = 2 xD/(x² – y²)
2 = (2 × x × 6)/(x² - 4²)
2(x² – 16) = 12x
x² - 6x - 16 = 0
x = 8, - 2
x = 8 km/h