Ratio & Proportion — CDS Elementary Mathematics PYQs

Let $x$, $y$, $z$ be variables such that $(x+y+z)=k$, where $k$ is a constant. If $(x+z-y)(x-z+y)$ is proportional to $yz$, then $(y+z-x)$ is proportional to:

A mixture of 100 L contains kerosene and turpentine oil in the ratio 3 : 2. What is the minimum quantity of kerosene in litres (whole number) that should be mixed in the mixture so that the resulting mixture has 20% of kerosene?

If $(x+y):(y+z):(z+x)=3:5:6$ and $x+y+z=14$, then what is $x^2+y^2+z^2$ equal to?

The ratio of sum of two numbers to their difference is 5 : 1. What is the ratio of the sum of their squares to the difference of their squares?

$X$ and $Y$ are two alloys of copper (Cu) and zinc (Zn). Alloy $X$ is prepared by mixing Cu and Zn in the ratio $5:4$, and alloy $Y$ is prepared by mixing Cu and Zn in the ratio $5:13$ respectively. If equal quantities of alloys $X$ and $Y$ are melted to form a third alloy $Z$, then what is the ratio of Cu to Zn in $Z$?

Two students $X$ and $Y$ appeared in a test. The score of $X$ is 20 more than that of $Y$. If the score of $X$ is 75% of the sum of the scores of $X$ and $Y$, then what is the ratio of score of $X$ to score of $Y$?

If $a:b:c:d=\sqrt{4}:\sqrt{3}:\sqrt{2}:\sqrt{1}$, then what is the value of $\frac{-a^2+b^2+c^2+d^2}{a^2-b^2+c^2-d^2}$?

If $m:n=1:2$ and $p:q=3:4$, then what is $(2m+4p):(n+3q)$ equal to?

A bottle contains spirit and water in the ratio $1:4$ and another identical bottle contains spirit and water in the ratio $4:1$. In what ratio should the mixtures in the two bottles be mixed to get a new mixture in which the ratio of spirit to water is $1:3$?

If $(a+b):(b+c):(c+a)=5:7:6$, then what is the value of $(a-b+c):(a+b-c)$?