If 5x = 30-y = 6z, then what is the value of (xy + yz + zx)/xyz?

If a + b + c = 9 and ab + bc + ca = 18, then what is the value of a3 + b3 + c3 – 3abc?

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

For an amount, simple interest at the rate of interest of 12% per annum for 6 years is Rs 25920. What will be the compound interest (in Rs) on same amount at the rate of interest of 8% per annum compounding annually for 2 years?

A bus travels 2/5 of a total journey at its usual speed. The remaining distance was covered by bus at 6/7 of its usual speed. Due to slow speed it reaches its destination 50 minutes late. If the total distance is 200 kms, then what is the usual speed (in km/hr) of bus?

How much water (in litres) must be added to 80 litres solution of milk and water containing 10% milk, so that it becomes a 5% milk solution?

A dealer sells two machines at Rs 12000 each. On one it gains 32% and on the other it looses 32%. What is its profit/loss percentage in the whole transaction?

The average age of a class of 6 girls is x years. Four new girls having ages x – 2, x + 2, x + 4 and x + 6 joins the class. What is the new average age (in years) of the class?