A boat takes 51 minutes to go 10.2 km upstream. The ratio of the speed of the boat in still water to that of the stream is 7:6. How much total time (in hours) will the boat take to go 17.7 km upstream and 66.3 km downstream?

3.4

2.1

1.9

0.3

APEDIA

RRB NTPC Graduate Tier 1

2025 • 05 Jun, 2025 • Shift-3

A boat takes 51 minutes to go 10.2 km upstream. The ratio of the speed of the boat in still water to that of the stream is 7:6. How much total time (in hours) will the boat take to go 17.7 km upstream and 66.3 km downstream?

Correct Answer

1.9

[Speed Discovery Phase]: First, calculate the upstream speed. Distance = 10.2 km, Time = 51 mins = 51/60 hours. Upstream Speed (U) = Distance / Time = 10.2 / (5......

💡 Analysis & Explanation

[Speed Discovery Phase] ▼

First, calculate the upstream speed. Distance = 10.2 km, Time = 51 mins = 51/60 hours. Upstream Speed (U) = Distance / Time = 10.2 / (51/60) = (10.2 × 60) / 51 = 612 / 51 = 12 km/hr.

[Ratio Application] ▼

Let the boat's speed in still water be 7x and the stream's speed be 6x. The upstream speed is essentially Boat - Stream, so 7x - 6x = x. Since U = 12 km/hr, we deduce x = 12. Consequently, the boat's speed is 84 km/hr and the stream's speed is 72 km/hr.

[Downstream Formulation] ▼

The downstream speed (D) is Boat + Stream = 84 + 72 = 156 km/hr.

[Final Time Calculation] ▼

Time required for 17.7 km upstream = 17.7 / 12 = 1.475 hours. Time required for 66.3 km downstream = 66.3 / 156 = 0.425 hours. Total journey time = 1.475 + 0.425 = 1.9 hours.

Conclusion ▼

The entire trip will consume exactly 1.9 hours.

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A boat takes 51 minutes to go 10.2 km upstream. The ratio of the speed of the boat in still water to that of the stream is 7:6. How much total time (in hours) will the boat take to go 17.7 km upstream and 66.3 km downstream?