With reference to a number greater than one, the difference between itself and its reciprocal is 25% of the sum of itself and its reciprocal. By how much percentage is the fourth power of the number greater than its square?

Find the value of - 

$\sqrt{2+\sqrt{3}} x \sqrt{2+\sqrt{2+\sqrt{3}}} x \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{3}}}} x \sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}$

A ship 77 km from the shore, springs a leak which admits $2\frac{1}{4}$ tones of water in $5\frac{1}{2}$ minutes. 92 tones of water would sink it. But the pumps can throw out 12 tons of water per hour. Find the average rate of sailing so that the ship may just reach the shore as it begins to sink.

In a mixture of milk and water, the proportion of milk by weight is 60%. If from the 80 gm mixture, 20 gm of mixture is taken out and 6 gm of pure water is added to the mixture, then find the ratio of milk and water in the new mixture.

In the figure, what is the area of $∆ABC if \frac{EC}{ED} =3 ?$