The mode of the following data is 67. Find the missing frequency x.

The median of the following data is 16. Find the missing frequencies a and b, if the total of the frequencies is 70.

If the angles of elevation of the top of the candle from two coins distant ‘a’ cm and ‘b’ cm (a>b) from its base and in the same straight line from it are 30° and 60°, then find the height of the candle.

The two palm trees are of equal heights and are standing opposite each other on either side of the river, which is 80 m wide. From a point O between them on the river the angles of elevation of the top of the trees are 60° and 30°, respectively. Find the height of the trees and the distances of the point O from the trees.

OR

The angles of depression of the top and bottom of a building 50 meters high as observed from the top of a tower are 30° and 60° respectively. Find the height of the tower, and also the horizontal distance between the building and the tower.

A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of the boat in still water and that of the stream.