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Minimum Distance for Round Boat Trip

XAT 2021 · Quantitative Ability & Data Interpretation · Medium · Arithmetic

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Swati can row a boat on still water at a speed of 5 km/hr. However, on a given river, it takes her 1 hour more to row the boat 12 km upstream than downstream. One day, Swati rows the boat on this river from X to Y, which is N km upstream from X. Then she rows back to X immediately. If she takes at least 2 hours to complete this round trip, what is the minimum possible value of N?

  1. A.

    3

  2. B.

    4.8

  3. C.

    2

  4. D.

    3.6

  5. E.

    2.1

Answer

B

Explanation

Let river speed be vv km/hr. Upstream speed = 5−v5 - v, Downstream speed = 5+v5 + v. Given: 125−v−125+v=1  ⟹  12(2v25−v2)=1  ⟹  24v=25−v2  ⟹  v2+24v−25=0  ⟹  v=1\frac{12}{5-v} - \frac{12}{5+v} = 1 \implies 12 \left(\frac{2v}{25-v^2}\right) = 1 \implies 24v = 25 - v^2 \implies v^2 + 24v - 25 = 0 \implies v = 1 km/hr. Upstream speed = 4 km/hr, Downstream speed = 6 km/hr. Round trip time for distance NN: T=N4+N6=5N12T = \frac{N}{4} + \frac{N}{6} = \frac{5N}{12}. Given T≥2  ⟹  5N12≥2  ⟹  N≥4.8T \ge 2 \implies \frac{5N}{12} \ge 2 \implies N \ge 4.8 km.

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