The speed of a boat while travelling downstream is 32 km per hour, whereas its speed while travelling upstream is 28 km per hour. What is the speed of the boat in still water?

Introduction / Context:
This is a classic boats and streams question from quantitative aptitude, testing your understanding of relative speed in still water and in a current. You are given the speed of the boat downstream and upstream and are required to find the speed of the boat in still water.

Given Data / Assumptions:
Downstream speed of the boat = 32 km per hour.
Upstream speed of the boat = 28 km per hour.
Let the speed of the boat in still water be b km per hour.
Let the speed of the stream be s km per hour.
Water current is uniform and the same in both directions.

Concept / Approach:
When a boat moves downstream, the current helps its motion, so downstream speed = b + s. When it moves upstream, the current opposes its motion, so upstream speed = b − s. If we know both downstream and upstream speeds, we can find b by adding the two equations and dividing by 2. This is a standard shortcut: speed in still water = (downstream speed + upstream speed) / 2.

Step-by-Step Solution:
Step 1: Write the downstream equation: b + s = 32. Step 2: Write the upstream equation: b − s = 28. Step 3: Add the two equations to eliminate s. This gives (b + s) + (b − s) = 32 + 28. Step 4: Simplify the left side to 2b, and the right side to 60, so 2b = 60. Step 5: Divide both sides by 2 to get b = 60 / 2 = 30. Step 6: Therefore, the speed of the boat in still water is 30 km per hour.

Verification / Alternative check:
You can find the speed of the stream as well to verify the calculation. From b + s = 32 and b = 30, we get s = 2 km per hour. Then b − s = 30 − 2 = 28 km per hour, which matches the given upstream speed. This confirms that b = 30 km per hour is correct.

Why Other Options Are Wrong:
27 km per hour would imply an average that is lower than both given speeds, which is impossible when you average 32 and 28.
29 km per hour would correspond to a downstream and upstream combination that does not match the given data.
31 km per hour is also inconsistent, because the average of 32 and 28 can be quickly estimated as exactly 30.
Only 30 km per hour is equal to (32 + 28) / 2, so it matches the formula.

Common Pitfalls:
Some learners mistakenly average 32 and 28 incorrectly, or they try to subtract instead of adding and dividing by 2. Others confuse the formula for speed of the stream, which is (downstream minus upstream) / 2, with the formula for the speed in still water. Remember: sum divided by 2 gives boat speed in still water, difference divided by 2 gives stream speed.

Final Answer:
The speed of the boat in still water is 30 km per hour.