For what value of ‘y’, $$ {x^{2}+{1\over12}{x}+y^{2}}$$ is perfect square?

If the area of a rhombus is 240 square feet if it's one diagonal is 16 feet, then what is the length (in meters) of the side of the rhombus?

Two equal glasses filled with mixture of milk and water in the proportions of 2 : 1 and 1 : 1 respectively are emptied into a third glass. What is the proportion of milk and water in the third glass?

In 80 litres mixture of milk and water the ratio of amount of milk to that of amount of water is 7: 3. In order to make this ratio 2: 1, how many litres of water should be added?

A, B and C alone can complete a piece of work in 24, 36 and 18 days respectively. A started working, after 2 days C joins with them and B joins with them after another 2 days, then find the no of days A, B and C worked together.

The perimeter of five squares are 24 cm, 32 cm, 40 cm, 76 cm and 80 cm respectively. The perimeter of another square equal in area to sum of the areas of these squares is: 

In a class, 60% speak Hindi and 70% speak English. If 28% of the students can’t speak any of the two languages, then what % of the students in the class can speak both the languages?

What is the area of an equilateral triangle having altitude equal to $$5\sqrt{3}$$cm.