The ratio of the speeds of the Boat Q to the Boat U in still water is 4 5 If the Boat U travels 126 ...........

Quantitative Aptitude ( CCS) Boats and Streams

Direction: Study the data carefully and answer the question given beside:
The table shows the distance travelled by five different boats upstream and downstream in same time and the line chart shows the speed of stream

The ratio of the speeds of the Boat Q to the Boat U in still water is 4 : 5. If the Boat U travels 126 km distance downstream and 81 km distance upstream in 7 hours 30 minutes, What is the speed of stream of Boat U?

15 km/h

10 km/h

20 km/h

12 km/h

None of these

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Explanation:

Speed of the Boat Q in still water = 24 km/h

Speed of the Boat U in still water =	24	× 5 = 30 km/h
	4

Let the speed of stream = x km/h
According to the question,

2 (3780 – 126x + 2430 + 81x) = 15 (900 – x²)

2 (6210 – 45x) = 13500 – 15x²

12420 – 90x = 13500 – 15x²

15x² – 90x – 1080 = 0

x²– 6x – 72 = 0

x² – 12x + 6x – 72 = 0

x (x – 12) + 6 (x – 12) = 0

(x + 6) (x – 12) = 0

x = –6, 12

Speed of stream = 12 km/h

Hence, option D is correct.