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1
When a, b, and x are positive and If a > b, then
$$\dfrac{a+x}{b+x}<\dfrac{a}{b}$$
2
When a, b, and x are positive and If a < b, then
$$\dfrac{a+x}{b+x}>\dfrac{a}{b}$$
3
a:b = b:c, then
$$b^2=ac$$
4
If x varies directly with y, then
$$x=ky$$, where ‘k’ is a proportionality constant
5
If x varies inversely with y, then
$$x=\dfrac{k}{y}$$, , where ‘k’ is a proportionality constant
6
If m and n are the values and a and b are the quantities of item 1 and item 2 respectively, and x is the weighted average of the two items, then
$$\dfrac{a}{b}=\dfrac{n-x}{x-m}$$
7
If there is a container with ‘a’ litres of liquid A and if ‘b’ litres are withdrawn and an equal amount of the mixture is replaced with another liquid B and if this operation is repeated ‘n’ times, then after the nth operation, Liquid A in the container equals
$$\left(\dfrac{a-b}{a+b}\right)^n$$ times the initial quantity of A.
8
If p and q are quantities of the cheaper and dearer items, r and s are the prices of the cheaper and dearer items, and t is the average price when they are mixed, then
$$\dfrac{p}{q}=\dfrac{s-t}{t-r}$$
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