$$ ({2+\sqrt{5}})$$ and $$ ({2-\sqrt{5}})$$ is a quadratic equation with roots.

simplify the following equation
$$ (1-{1\over3})(1-{1\over4})(1-{1\over5})......(1-{1\over n})$$

A man spends $$ {2\over3}rd$$ of his income. If his income increases by 14 % and the expenditure increases by 20%, then the percentage increase in his savings will be

What will be come in place of question mark(?) in the following number series?
8,  14, 25, 46, 82 , ?

Nisha bought a number of oranges at 2 for a rupee and an equal number at 3 for a rupee. To make a profit of 20% she should sell a dozen for

A vendor sells potatoes at a cost price, but he mixes some rotten potatoes and thereby gains 25%. The percentage of rotten potatoes in the mixture is? 

The distance between the centers of two circles having radii 4.5 cm. and 3.5 cm. respectively is 10 cm. What is the length of the transverse common tangent of these circles?

Direction: Study the following table carefully and answer the given questions. Table shows the of passed students in four schools and ratio between passed boys and girls among them. The ratio between failed boys and girls is reverse of passed ratio between them.

If the difference between the failed boys and girls is 25 in school S, then find the ratio between passed and failed students in School S?