ABC is triangle in which AB = 3 cm, BC= 5 cm and AC = 4 cm. AD is a perpendicular from A to BC. Find the length of AD.

The ratio of the ages of a man and his wife is 4 : 3. After 4 years, the ratio will be 9:7. If at the time of marriage the ratio was 5: 3, then how many years ago were they married?

A trader, while selling an item, was asking for such a price that would enable him to of, a 20% discount and still make a profit of 30% on cost. If the cost of the item was Tk. 50 what was his asking price?

$if x+y=a, x^2+y^2 and x^3+y^3=c^3 then show that a^3+2c^3=3a{b}^2$

Solve the following Problem: 

The average age of a committee of 8 members is 40 years. A member aged 55 years retired and his place was taken by another number aged 39 years. What will be the average age of the present committee?