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Question Paper from: SBI PO Prelims 2017

A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is:

14 km/hr

10 km/hr

6 km/hr

4 km/hr

3 km/hr

Solution:

Chapter Name: Boats and Stream

Let the speed of the boat in still water be x km/hr and the speed of the stream be y km/hr.

Then,

Speed upstream = (x - y) km/hr, Speed downstream = (x + y) km/hr.

$\frac{24}{x - y}$ + $\frac{28}{x + y}$ = 6

⇒ 24a + 28b = 6, where x - y = $\frac{1}{a}$ and x + y = $\frac{1}{b}$

⇒ 12a + 14b = 3

$\frac{30}{x - y}$ + $\frac{21}{x + y}$ = $\frac{13}{2}$

⇒ 60a + 42b = 13

On solving (i) and (ii), we get : 28b = 2

⇒ b = $\frac{1}{14}$ and a = $\frac{1}{6}$

$∴$ (x - y) = 6 and x + y = 14)

⇒ x = 10, y = 4

Speed of the boat in still water = 10 km/hr.

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SBI PO Prelims 2017

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