All Exams Test series for 1 year @ ₹349 only
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.

Was this answer helpful?

Important Questions from Boat and River

  1. A boat sails 15 km of a river towards upstream in 5 hours. How long (in hours) will it take to cover the same distance downstream, if the speed of river is one-fourth the speed of the boat in still water?

  2. The speed of boat upstream is 5 kmph. Its speed in still water is 10 kmph. How many minutes will it take to row 25 km downstream?

  3. 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?

  4. The downstream speed of a boat is 20 km/hr and the speed of stream is 4 km/hr. What will be the total time taken by the boat to cover 160 km downstream and 96 km upstream?

  5. The ratio of the speeds of a boat in still water and the speed of the river is 3 ∶ 1. The boat takes 45 minutes for a round trip journey. Find the distance of the whole trip if the speed of the stream is 4 km/hr.

Need Expert Advice?
Test Series
CDS img
Defence
UPSC CDS 2026 Mock Test Series
536 Tests 4 Tests Free
1633 Attempts
4.3(174)
English, Hindi
More Questions from CDS

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App