Question

A boat goes 96 km upstream in 8 hours and covers the same distance moving downstream in 6 hours. On the next day, the boat starts from point A, goes downstream for 1 hour, then upstream for 1 hour and repeats this four more times, that is, 5 upstream and 5 downstream journeys. Then the boat would be:

• A. 22.5 km downstream of A
• B. 15 km downstream of A
• C. 12.5 km downstream of A
• D. 20 km downstream of A

Hint:

For problems involving upstream and downstream motion, use the formula for speed, \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \), to find the boat's speed in still water and the speed of the stream.

Answer 1

The Correct Option is D

Step 1: Let the speed of the boat in still water be \( b \) km/h and the speed of the stream be \( s \) km/h. The boat goes 96 km upstream in 8 hours and covers the same distance downstream in 6 hours. The effective speed upstream is \( b - s \) and downstream is \( b + s \). Using the given times: \[ \frac{96}{b - s} = 8 \quad \text{and} \quad \frac{96}{b + s} = 6. \] Solving these equations: \[ b - s = \frac{96}{8} = 12 \quad \text{and} \quad b + s = \frac{96}{6} = 16. \] By adding and subtracting these equations, we find: \[ b = \frac{12 + 16}{2} = 14 \quad \text{and} \quad s = \frac{16 - 12}{2} = 2. \] Step 2: Calculate the total distance covered in 10 journeys. In one upstream and one downstream journey, the boat covers a total distance of: \[ \text{Distance in 1 round trip} = (b + s) + (b - s) = 16 + 12 = 28 \, \text{km}. \] In 5 such round trips, the total distance covered is: \[ \text{Total distance} = 5 \times 28 = 140 \, \text{km}. \] Since the boat starts from point A and ends after 10 trips, the boat is 20 km downstream of A. Thus, the correct answer is (D).