Question
Determine the speed of a Ship in calm water, given that
the Ship's speed downstream is 20% greater than its speed in still water. If the Ship can cover 48 km both upstream and downstream in a total of 5 hours, what is the speed of the Ship in still water?Solution
ATQ, Let speed of Ship in still water is ‘5a’ km/h Speed of Ship in downstream = 1.20 × 5a = 6a Speed of stream = 6a – 5a = a km/h Speed of Ship in upstream = 5a – a = 4a km/h So, (48/6a) + (48/4a) = 5 Or, (8/a) + (12/a) = 5 Or, a = (8 + 12)/5 = 4 Speed of Ship in still water = 5 × 4 = 20 km/hr
If a + b = 56 and (a – b)² = 496, find the value of the product of a and b.
In △ ABC, AB = AC. A circle drawn through B touches AC at D and intersect AB at P. If D is the midpoint of AC and AP = 2.5 cm, then AB is equal to:
1/3 + 1/15 + 1/35 + 1/63 + 1/99 = ?
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