Two straight lines pass through the origin (x₀, y₀) = (0, 0). One of them passes through the point (x₁, y₁) = (1, 3) and the other passes through the point (x₂, y₂) = (1, 2). What is the area enclosed between the straight lines in the interval [0, 1] on the x-axis?

If

p : q = 1 : 2

q : r = 4 : 3

r : s = 4 : 5

and u is 50% more than s, what is the ratio p : u?

In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is

P invested Rs.5000 per month for 6 months of a year and Q invested Rs. x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year. If at the end of that investment year, Q receives $${4 \over 9}$$ of the total profit, what is the value of (in Rs.)?