Quantitative Aptitude - Arithmetic Ability Questions

A ladder 13 m long reaches a window which is 12 m above the ground on side of a street. Keeping its foot at the same point, the ladder is turned to the other side of the street to each a window 5m high, then the width of the street is :

x, y and z are real numbers. If x3 + y3 + z3 = 13, x + y + z = 1 and xyz = 1, then what is the value of xy + yz + zx?

If x + y + z = 0, then what is the value of (3y2 + x2 + z2 )/(2y2 – xz)?

Find the fraction which bears the same ratio to 1/27 that 3/7 does to 5/9 .

Given: 6x + 2(6-x) > 2x -2 < 5x/2 - 3x/4; then x can take which of the following values?

ΔPQR is right angled at Q. If cotP = 5/12, then what is the value of tanR ?

A thief is stopped by a policeman from a distance of 200 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed
of the thief as 8 km/hr and that of police man as 10 km/hr. How far the thief would have run, before he is over ­taken?

John is 15 years younger than Jill, 12 years ago, Jill's age was 1.5 times that of John. Jill is now ___ years old.