Point A(x, y) divides segment BC with coordinates B (2, 3) & C (7, 8) in the ratio 2: 3. What is the value of (x, y)? 

Angles of elevation of top of a tower having base O, from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° & 60° respectively. Then ratio AB : BC is

Preferences of people (man & children) in buying different ice cream flavors:

People buying chocolate ice cream in year 2001 & 2002 together are approximately what percent more or less than people buying vanilla flavor in 2004 & 2005 together? 
 

Preferences of people (man & children) in buying different ice cream flavors:

What is the ratio of people buying vanilla flavor in 2001, 2004 & 2005 to the people buying strawberry flavor over all the years? 

Preferences of people (man & children) in buying different ice cream flavors:

Average of people buying vanilla flavor in 2004 & 2005 together is X & if people buying chocolate flavor in 2006 are 100/11% more than X. Find no. of people buying chocolate flavor in 2007. 

Preferences of people (man & children) in buying different ice cream flavors:

What is the ratio of people who liked strawberry flavor in year 2001, 2003 & 2005 to the people who liked vanilla & strawberry flavor in the year 2002 & 2004. 

If α and β are roots of the equation 3x² - 13x + 14 = 0 then what is the value of (α/β) + (β/α)? 

A ∆ABC has sides, AB, BC & CA that measure 13, 14 and 15 units respectively. A line EF ⊥ to the side of measure 14 units divides the interior of the ∆ABC into two regions of equal area as shown in figure. Find the length of EF?