Let us write some equations for practice:
1$A$ exceeds $B$ by 100
2$A$ is 50 more than $B$
3$A$ is 75 less than $B$
4$A$ is twice that of $B$
5$A$ is one third of $B$
6$A$ is 25% less than $B$
\begin{array}{lrl}
\Rightarrow & A & = 75\% (B) \\[4px]
&A & =\left( {1 - \dfrac{25}{100}} \right)B\\[4px]
&A & =\left( {1 - \dfrac{1}{4}} \right)B\\[4px]
\end{array}
$
7$A$ is 20% more than $B$
\begin{array}{lrl}
\Rightarrow & A & = 120\% (B)\\[4px]
&A & =\left( {1 + \dfrac{20}{100}} \right)B\\[4px]
&A & =\left( {1 + \dfrac{1}{5}} \right)B\\[4px]
\end{array}
$
Let us learn how to take variables for the unknowns while solving equations:
1 $A$ exceeds $B$ by 100
2 $A$ is 50 more than $B$
3 $A$ is twice that of $B$
4 Consecutive numbers:
5 Consecutive even numbers:
6 Consecutive odd numbers:
General Formulas:
1 \({a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)\)
2 \({\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\)
3 \({\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\)
4 \({\left( {a + b} \right)^2} = {\left( {a - b} \right)^2} + 4ab\)
Formulas related to Series:
Formula: 1
Sum of the first $n$ natural numbers = $\dfrac{{n\left( {n + 1} \right)}}{2}$
Formula: 2
Sum of the first $n$ natural number squares = $\dfrac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}$
Formula: 3
Sum of the first $n$ natural number cubes = ${\left( {\dfrac{{n\left( {n + 1} \right)}}{2}} \right)^2}$
Formula: 4
Sum of the first $n$ odd numbers = ${n^2}$
Formula: 5
Sum of the first $n$ even numbers = ${n\left( {n + 1} \right)}$
Formula: 6
Sum of the terms in an Arithmetic Progression (A.P) =
$\begin{array}{rl}
{S_n} & =\dfrac{n}{2}\left( {2a + \left( {n - 1} \right)d} \right) \\[5px]
&=\dfrac{n}{2}\left( {a + l} \right) \\[4px]
\end{array}
$
Here,
Formula: 7
Number of terms in an Arithmetic Progression (A.P) = $n = \dfrac{{l - a}}{d} + 1$
