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A lighthouse is a tall tower with light ...

A lighthouse is a tall tower with light near the top. These are often built on islands, coasts or on cliffs. Lighthouses on water surface act as a navigational aid to the mariners and send warning to boats and ships for dangers. Initially wood, coal would be used as illuminators. Gradually it was replaced by candles, lanterns, electric lights. Nowadays they are run by machines and remote monitoring.
Prongs Reef lighthouse of Mumbai was constructed in 1874-75. It is approximately 40 meters high and its beam can be seen at a distance of 30 kilometres. A ship and a boat are coming towards the lighthouse from opposite directions. Angles of depression of flash light from the lighthouse to the boat and the ship are `30^(@)` and `60^(@)` respectively.

Find the mean age of the passengers.
i) Which of the two, boat or the ship is nearer to the light house. Find its distance from the lighthouse?
ii) Find the time taken by the boat to reach the light house if it is moving at the rate of 20 km per hour.

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