Ratio & Proportion — CDS Elementary Mathematics PYQs

If $x$ varies directly as $y$, then which of the following is/are correct?
I. $(x^2+y^2)$ varies directly as $y^2$.
II. $\left(\frac{x^3}{y^4}\right)$ varies directly as $y$.

Select the answer using the code given below:

The ratio of the present age of $X$ to that of $Y$ is $4:5$. $k$ (less than 10) years ago, this ratio was $1:2$. How many values of $k$ are possible if the ages are expressed in complete years?

A locomotive engine can go 40 km/hr. Its speed gets reduced by a quantity that varies directly as the square root of the number of wagons attached. It is known that its speed becomes 16 km/hr if 36 wagons are attached. What is the smallest number of wagons with which the engine is unable to move?

Two numbers $P$ and $Q$ are such that $P:Q=x:y$. If 1 is added to both the numbers, the ratio becomes $7:10$. If 3 is added to both the numbers, the ratio becomes $3:4$. What is $(x+y):(x-y)$ equal to?

Consider the following for the next two (02) items:
$X$ is an alloy of copper and zinc. $Y$ is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of $X$ and $Y$ is found to contain 74% of copper, 16% of zinc and 10% of tin.

What is the percentage of copper in $X$?

Consider the following for the next two (02) items:
$X$ is an alloy of copper and zinc. $Y$ is an alloy containing 80% of copper, 4% of zinc and 16% of tin. A fused mass of $X$ and $Y$ is found to contain 74% of copper, 16% of zinc and 10% of tin.

What is the percentage of zinc in $X$?

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?