An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing East.

The ant first turns 72$$^\circ$$ anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting.

1. moves forward for 10 cm.

2. turns 144$$^\circ$$ clockwise

The pattern made by the trade left behind by the ant is

In a partnership business the monthly investment by three friends for the first six months is in the ratio 3 : 4 : 5. After six months, they had to increase their monthly investments by 10%, 15% and 20%, respectively, of then initial monthly investment. The new investment ratio was kept constant for the next six months.

What is the ratio of their shares in the total profit (m the same order) at the end of the year such that the share is proportional to their individual total investment over the year?

A survey of 450 students about their subjects of interest resulted in the following outcome.

$$\bullet$$ 150 students are interested in Mathematics.

$$\bullet$$ 200 students are interested in Physics.

$$\bullet$$ 175 students are interested in Chemistry.

$$\bullet$$ 50 students are interested in Mathematics and Physics.

$$\bullet$$ 60 students are interested in Physics and Chemistry.

$$\bullet$$ 40 students are interested in Mathematics and Chemistry.

$$\bullet$$ 30 students are interested in Mathematics, Physics and Chemistry.

$$\bullet$$ Remaining students are interested in Humanities.

Based on the above information, the number of students interested in Humanities is

$$x:y:z = {1 \over 2}:{1 \over 3}:{1 \over 4}$$

What is the value of $${{x + z - y} \over y}$$ = ?