Upstream and downstream boat speed

CMAT 2018 · Quantitative Techniques & Data Interpretation · Medium · Speed Time Distance

A boat covers 24 km upstream and 72 km downstream in 8 hours, while it covers 48 km upstream and 108 km downstream in 14 hours. Find the speed of the boat in still water and the speed of the stream respectively.

  1. A.

    12 km/h, 6 km/h

  2. B.

    10 km/h, 5 km/h

  3. C.

    10 km/h, 6 km/h

  4. D.

    12 km/h, 5km/h

Answer

A

Explanation

Let upstream speed be uu and downstream speed be vv. 24u+72v=8\frac{24}{u} + \frac{72}{v} = 8 48u+108v=14\frac{48}{u} + \frac{108}{v} = 14

Multiplying the first equation by 2: 48u+144v=16\frac{48}{u} + \frac{144}{v} = 16

Subtracting the second equation: 36v=2  ⟹  v=18 km/h.\frac{36}{v} = 2 \implies v = 18\text{ km/h.} Substitute v=18v = 18 into first equation: 24u+4=8  ⟹  u=6 km/h.\frac{24}{u} + 4 = 8 \implies u = 6\text{ km/h.}

Speed of boat in still water = 18+62=12\frac{18 + 6}{2} = 12 km/h. Speed of stream = 18−62=6\frac{18 - 6}{2} = 6 km/h.

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