(i) Consider the monthly pocket money of Ravi and Sanjeev as \[5x\] and \[7x\]
Their expenditure is \[3y\] and \[5y\] respectively.
\[5x\text{ }\text{ }3y\text{ }=\text{ }80\] …… (1)
\[7x\text{ }\text{ }5y\text{ }=\text{ }80\] …… (2)
Now multiply equation (1) by \[7\] and (2) by \[5\]
Subtracting both the equations
\[\begin{array}{*{35}{l}}
35x\text{ }\text{ }21y\text{ }=\text{ }560 \\
35x\text{ }\text{ }25y\text{ }=\text{ }400 \\
\end{array}\]
So we get
\[\begin{array}{*{35}{l}}
4y\text{ }=\text{ }160 \\
y\text{ }=\text{ }40 \\
\end{array}\]
In equation (1)
\[\begin{array}{*{35}{l}}
5x\text{ }=\text{ }80\text{ }+\text{ }3\text{ }\times \text{ }40\text{ }=\text{ }200 \\
x\text{ }=\text{ }40 \\
\end{array}\]
Here the monthly pocket money of Ravi = \[5\text{ }\times \text{ }40\text{ }=\text{ }200\]
(ii) Consider x as the number of students in class
Ratio of boys and girls = \[4:3\]
Number of boys = \[4x/7\]
Number of girls = \[3x/7\]
Based on the problem
\[\left( 4x/7\text{ }+\text{ }20 \right):\text{ }\left( 3x/7\text{ }\text{ }12 \right)\text{ }=\text{ }2:\text{ }1\]
We can write it as
\[\left( 4x\text{ }+\text{ }140 \right)/\text{ }7:\text{ }\left( 3x\text{ }\text{ }84 \right)/\text{ }7\text{ }=\text{ }2:\text{ }1\]
So we get
\[\begin{array}{*{35}{l}}
\left( 4x\text{ }+\text{ }140 \right)/\text{ }7\text{ }\times \text{ }7/\text{ }\left( 3x\text{ }\text{ }84 \right)\text{ }=\text{ }2/1 \\
\left( 4x\text{ }+\text{ }140 \right)/\text{ }\left( 3x\text{ }\text{ }84 \right)\text{ }=\text{ }2/1 \\
6x\text{ }\text{ }168\text{ }=\text{ }4x\text{ }+\text{ }140 \\
6x\text{ }\text{ }4x\text{ }=\text{ }140\text{ }+\text{ }168 \\
2x\text{ }=\text{ }308 \\
x\text{ }=\text{ }308/2\text{ }=\text{ }154 \\
\end{array}\]
Therefore, \[154\] students were there in the class.