SBI PO Prelims 8 Mar 2025 Shift 1 Paper

Concept:The average speed of a boat in a stream is the harmonic mean of its upstream and downstream speeds.Explanation:Let the speed of the stream be $3x$ km/hr and the upstream speed be $7x$ km/hr.Speed in still water = upstream speed + stream speed = $7x + 3x = 10x$ km/hr.Downstream speed = still water speed + stream speed = $10x + 3x = 13x$ km/hr.Average speed is given as $9.1$ km/hr, which equals the harmonic mean:$$\frac{2 \times 7x \times 13x}{7x + 13x} = 9.1$$This simplifies to $\frac{182x^2}{20x} = 9.1$, so $9.1x = 9.1$, giving $x = 1$.Thus, stream speed $= 3$ km/hr, boat speed in still water $= 10$ km/hr, upstream $= 7$ km/hr, and downstream $= 13$ km/hr.Time downstream for $(D+23)$ km $= \frac{D+23}{13}$ hours.Time upstream for $(1.2D - 27)$ km $= \frac{1.2D - 27}{7}$ hours.Sum of these times is 60 hours: $\frac{D+23}{13} + \frac{1.2D - 27}{7} = 60$.Multiply by 91: $7(D+23) + 13(1.2D - 27) = 5460$.This gives $7D + 161 + 15.6D - 351 = 5460$, so $22.6D - 190 = 5460$.Hence $22.6D = 5650$, and $D = 250$ km.Time to cover $D$ km in still water $= \frac{250}{10} = 25$ hours.Answer:25 hours (Option B).