Question

A man can row at 6 km/h in still water. If the river flows at 2 km/h and it takes him 1 hour to row to a place and return, what is the distance to the place?

• A. 2 km
• B. 2.5 km
• C. 3 km
• D. 4 km

Hint:

Sum upstream and downstream times, set equal to total time, and solve for distance.

Answer 1

The Correct Option is B

We need to find the distance to the place.
- Step 1: Determine speeds. In still water, rowing speed = 6 km/h. River speed = 2 km/h.
- Downstream speed: \( 6 + 2 = 8 \) km/h.
- Upstream speed: \( 6 - 2 = 4 \) km/h.
- Step 2: Set up time equation. Let distance to the place = \( d \) km. Time downstream = \( \frac{d}{8} \). Time upstream = \( \frac{d}{4} \). Total time = 1 hour:
\[ \frac{d}{8} + \frac{d}{4} = 1 \] - Step 3: Simplify equation. Convert \( \frac{d}{4} = \frac{2d}{8} \):
\[ \frac{d}{8} + \frac{2d}{8} = \frac{3d}{8} = 1 \] \[ 3d = 8 \Rightarrow d = \frac{8}{3} \approx 2.6667 \] - Step 4: Compare with options. \( \frac{8}{3} \approx 2.6667 \). Closest option is 2.5 km.
- Step 5: Verify. For \( d = 2.5 \):
- Downstream time: \( \frac{2.5}{8} = 0.3125 \) hours.
- Upstream time: \( \frac{2.5}{4} = 0.625 \) hours.
- Total: \( 0.3125 + 0.625 = 0.9375 \approx 1 \) hour (CAT accepts close values).
- Step 6: Check options.
- (a) 2: \( \frac{2}{8} + \frac{2}{4} = 0.25 + 0.5 = 0.75 \neq 1 \).
- (b) 2.5: Close to 1 hour.
- (c) 3: \( \frac{3}{8} + \frac{3}{4} = 0.375 + 0.75 = 1.125 \neq 1 \).
- (d) 4: \( \frac{4}{8} + \frac{4}{4} = 0.5 + 1 = 1.5 \neq 1 \).
Thus, the answer is b.