CDS 2026 (I) Elementary Mathematics, question 18

Topic: Arithmetic (percentage, ratio, interest, time and work, speed)

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Q18

A person goes downstream at xx km/h and upstream at yy km/h by the same boat. What is the ratio of speed of boat in still water to speed of water ?

  1. (a) xy\frac{x}{y}
  2. (b) yx\frac{y}{x}
  3. (c) (x+y)(x−y)\frac{(x+y)}{(x-y)}Correct answer
  4. (d) (x−y)(x+y)\frac{(x-y)}{(x+y)}

Solution.

Answer: (c) (x+y)(x−y)\frac{(x+y)}{(x-y)}

  1. Let the boat's still-water speed be b and the current speed be c.
  2. Then b+c=xb + c = x and b−c=yb - c = y, so b=(x+y)/2b = (x + y)/2 and c=(x−y)/2c = (x - y)/2.