WBCS Mains 2020 Official Paper-VI

If $x=by+cz$, $y=cz+ax$, and $z=ax+by$, then the value of the expression:
$$\frac{a}{1+a}+\frac{b}{1+b}+\frac{c}{1+c}$$

is equal to:

The age of a father today is thrice as that of his son. After $15$ years, the age of the father will be twice that of his son. The age of the son today is:

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio $8:5$, the ratio of radius to the height is:

$ABCD$ is a cyclic quadrilateral and the sides $DC$ and $AB$ are produced to meet at $P$. If $\angle APD=25^{\circ }$ and $\angle PBC=70^{\circ }$, then $\angle BAD$ is equal to:

The price of coal being increased by $20\%$, a family reduces its consumption of coal by $20\%$. By what percent will the family's expenses for coal increase or decrease?