Vinay and Versha run a race with their speed in the ratio of 5 : 3. They prefer to run on a circular track of circumference 1.5 km. What is the distance covered by Vinay when he passes Versha for the seventh time?

When do the two hands of a clock of just after 3 pm make 30°angel between them?

Two boats go downstream from point X to Y. The faster boat covers the distance from X to Y, 1.5 times as fast as slower boat. It is known that for every hour slower boat lags behinds the faster boat by 8 km. however, if they go upstream, then the faster boat covers the distance from Y to X in half the time as the slower boat. Find the speed of the faster boat in still water?

A dog after traveling 50 km meets a swami who counsels him to go slower. He then proceeds at $$\frac{3}{4}$$ of his former speed and arrives at his destination 35 min late. Had the meeting occurred 24 km further the dog would have reached its destination 25 min late. The speed of dog is:

A girl while walking diametrically across a semicircular playground, takes 3 minutes less than if she had kept walking round the circular path from A to B. If she walks 60 metres a minute, what is diameter of the play ground?

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