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The angle of elevation of an aeroplane from point A on the ground is 60°. After flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 1500√3 m, find the speed of the plane in km/hr.
Joseph bought two woollen jackets for Rs. 2,100 and Rs. 3,150, respectively. By selling the first at a gain of k% and the second at a loss of k%, he found that the selling price of both is the same. What is the value of k?
The speed of a boat in still water is 25 km/h. It takes \(33\frac{1}{3}\) % more time to cover a certain distance in still water than to cover the same distance downstream. How much time (in hours) will the boat take to go 75 km downstream?
The rate of simple interest on a sum of money is 5% p.a. for the first 4 years, 8% p.a. for the next 3 years and 10% p.a. for the period beyond 7 years. If the simple interest accrued by the sum over a period of 10 years is Rs.1,850, then the sum is :
A, B and C can complete a certain work in 30 days. B and C together can complete the same work in 45 days. If B is 20% more efficient than A, then B alone can complete one-third of the same work in: