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Directions: Each question below contains a statement followed by two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.
Quantity I: A boat running downstream covers a distance of 20 km in 4 hrs, while for covering the same distance upstream it takes 5 hrs. Speed of boat in still water (in kmph).
Quantity II. A boat can cover a distance of 48 km in 3 hrs in still water. If speed of current is 4 kmph, then the difference between time of boat to cover the same distance upstream (in hrs).
QI > QII
QI < QII
QI ≤ QII
QI ≥ QII
Cannot be determined
- Quantity I:
- Downstream speed: \( \frac{20 \text{ km}}{4 \text{ hrs}} = 5 \text{ kmph} \).
- Upstream speed: \( \frac{20 \text{ km}}{5 \text{ hrs}} = 4 \text{ kmph} \).
- Speed of boat in still water (B) = \( \frac{(\text{Downstream speed} + \text{Upstream speed})}{2} = \frac{(5 + 4)}{2} = 4.5 \text{ kmph} \).
- Quantity II:
- Boat speed in still water: \( \frac{48 \text{ km}}{3 \text{ hrs}} = 16 \text{ kmph} \).
- Difference in time upstream:
- Upstream speed = \( (16 - 4) \) kmph = 12 kmph.
- Time upstream: \( \frac{48 \text{ km}}{12 \text{ kmph}} = 4 \text{ hrs} \).
- Difference = \( 4 \text{ hrs} - 3 \text{ hrs} = 1 \text{ hr} \).
- Comparison:
- Quantity I (4.5) vs. Quantity II (1).
- Answer: Quantity I > Quantity II.
By: Parvesh Mehta ProfileResourcesReport error
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