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Question

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

This question was previously asked in
CDS 2 2026 Maths Question Paper (13-Sep-2026)
The correct answer is
\(\frac{(x+y)}{(x-y)}\)

Understanding Boat Speed Ratio Calculation

The problem asks for the ratio of the speed of the boat in still water to the speed of the water. We are given the speed downstream (\(x\)) and the speed upstream (\(y\)).

Formulating Speed Equations

Let:

  • \(B\) = Speed of the boat in still water (km/h)
  • \(C\) = Speed of the water current (km/h)

We know the following relationships:

  • Speed downstream = Speed of boat + Speed of water
  • Speed upstream = Speed of boat - Speed of water

Using the given variables:

  • \(B + C = x\) (Equation 1: Speed downstream)
  • \(B - C = y\) (Equation 2: Speed upstream)

Calculating Speed of Boat and Water

To find the speed of the boat (\(B\)) and the speed of the water (\(C\)), we can solve the system of linear equations:

  1. Add Equation 1 and Equation 2: \((B + C) + (B - C) = x + y\) \(2B = x + y\) \(B = \frac{x + y}{2}\)
  2. Subtract Equation 2 from Equation 1: \((B + C) - (B - C) = x - y\) \(2C = x - y\) \(C = \frac{x - y}{2}\)

Deriving the Speed Ratio

The question requires the ratio of the speed of the boat in still water (\(B\)) to the speed of the water (\(C\)).

Ratio = \(\frac{B}{C}\)

Substitute the values we found for \(B\) and \(C\):

\(\text{Ratio} = \frac{\frac{x + y}{2}}{\frac{x - y}{2}}\)

Simplify the expression:

\(\text{Ratio} = \frac{x + y}{x - y}\)

This matches Option 3.

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Important Questions from Boat and River

  1. Sudha can travel a certain distance downstream in 6 hours by boat and return to the starting point in 9 hours. If the stream flows at a speed of 3 km/h, how long (in hours) will it take to cover a distance of 67.5 km in still water?

  2. A man covered a distance of 18 km in 3 hours, 7.2 km in 2 hours and 15 km in 5 hours. What is the average distance traveled by him per hour?

  3. A boat covers 20 km upstream and 60 km downstream in 5 hours. Boat covers 30 km upstream and 80 km downstream in 7 hours. What is the speed of boat in still water?

  4. Dalip can row 42 km downstream in 2 hours and the same distance upstream in 2 hours and 48 minutes. How much time will he take to row 31.5 km downstream and 22.5 km upstream?

  5. A boat covers a distance of 2 km upstream and 4 km downstream in 120 minutes. It covers a distance of 4 km upstream and 6 km downstream in 210 minutes. What is the speed of the boat in still water?

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