In ΔABC, ∠C=90° and D is a point on CB such that AD is the bisector of ∠A. If AC=5 cm and BC=12 cm, then what is the length of AD?

The speed of train A is 16 km/h less than the speed of train B. To cover a distance of 384 km, B takes 4 hours less time than A. What is the speed (in km/h) of train B?

A person rows a distance of $$ {3{3\over4}{ \ km}}$$ upstream in $$ {1{1\over 2}{\ hours}}$$ and a distance of 13 km downstream in 2 hours. How much time ( in hours) will the person take to row a distance of 90 km in still water?

If the 5 digit number 538xy is divisible by 3, 7 and 11, then the value of (x² +y²)  is:

Let x be the least number divisible by 13, such that when x is divided by 4, 5, 6, 7, 8 and 12, the remainder in each case is 2. The sum of the digits of x is:

Pipes  A and B are emptying pipes and can empty a tank in 6 hours and 16 hours, respectively. C is a filling a pipe. All the three pipes were opened together. They took 80 minutes to empty $$ {5\over 8}th$$ of the tank. Pipe C alone can fill the tank in:

Seven year ago, the ages (in years) of A and B were in the ratio 4 : 5 and 7 years hence, their ages will be in the ratio 5 : 6. What will be the ratio of their ages 5 years from now?

ABCD is cyclic quadrilateral Sides AB and DC, when produced, meet at E, and sides BC and AD, When produced, meet at F. If ∠BFA=60° and ∠AED=30°, then the measure of ∠ABC is: