Question

A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current.

A
9 km/hr, 6 km/hr
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B
5 km/hr, 3 km/hr
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C
8 km/hr, 3 km/hr
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D
8 km/hr, 5 km/hr
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Solution

The correct option is C 8 km/hr, 3 km/hrLet the speed of man in still water be x km/hr and speed of current be y km/hr. Speed upstream = (x - y)km/hr and speed downstream = (x + y)km/hr. 40x−y+55x+y=13 and 30x−y+44x+y=10Let 1x−y=u and 1x+y=v So equations become 40u+55v=13 and 30u+44v=10 On writing the equations in standard form, we get 40u+55v−13=0 30u+44v−10=0 By cross multiplication, we get u55×(−10)−44×(−13)=v30×(−13)−40×(−10)=144×40−55×30⇒ u−550+572=v−390+400=11760−1650⇒ u22=v10=1110⇒ u=22110=15 and v=10110=111 So, u=15=1x−y⇒x−y=5 . . . (1) and v=111=1x+y⇒x+y=11 . . . (2) On adding (1) & (2), we get 2x=16 ⇒ x=8 and putting x = 8 in (1), we get, 8−y=5 ⇒ y=3. ∴ Speed of man in still water is 8 km/hr and speed of the current is 3 km/hr.

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