A bus can travel a distance of 1330 Km in 19 hours. Speed of a bike is 50% less than the speed of the bus and speed of a cycle is 15 Km/h less than the speed of the bike. Find the respective ratio of the time taken by cycle and bike to cover a distance of 280 km.

Direction: In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x² – 2x - 8 = 0
II. y² – 7y - 60 = 0

Some students went on a field trip. At a speed of 6 km/h, they travelled by bikes for 2 hours; then at a speed of 2 km/h, they walked for another hour; then they took rest for an hour and had lunch for half an hour; then at a speed of 1 m/s, they walked for an hour to visit a garden; and finally at a speed 4 km/h, they returned home in 3 hours. Their average speed, in km/h, (rounded off to two places of decimal) is:

An item costing Rs. 840 was sold by a shopkeeper at a gain of 10 % and it was again sold by the new buyer at a loss of 5 %. Find selling price of the item is: 

What is the simplification value of $${cotA+tanB}\over{cotB+tanA}$$?

The third proportional of two numbers 4 and 20 is

A square and an equilateral triangle are of the same perimeter. If the diagonal of the square is $$ {12\sqrt{2}}$$ cm long, then the area of the triangle is.

$${I.{(13)^{2}}-14+28=x}$$
$${II.{(16)^{2}}-8×7=y}$$