Question

The ratio of incomes of Salim and Jawed was 20:11. Three years later income of Salim has increased by 20% and income of Jawed has increased by Rs.500. Now the ratio of their income becomes 3:2. Find original incomes of Salim and Jawed.

Answer 1

Hint: In this problem, first we need to consider the income of Salim and Jawed in one variable. Now, find the income of Salim and Jawed after 3 years. Take the ratio of income of Salim and Jawed after 3 years and put it equal to 3:2.

Complete step-by-step answer:
Consider, the income of Salim be \[ 20x\] and income of Jawed be\[11x\].
Since, the income of Salim has increased by 20% after 3 years; the income of Salim after 3 years can be calculated as shown below.
\[
  \,\,\,\,\,\,{\text{Income of Salim}} = 20x + 20x \times \dfrac{{20}}{{100}} \\
   \Rightarrow {\text{Income of Salim}} = 20x + 4x \\
   \Rightarrow {\text{Income of Salim}} = 24x \\
\]
Similarly, the income of Jawed has increased by Rs.500 after 3 years. Therefore, the income of Jawed after 3 years can be calculated as shown below.
\[{\text{Income of Jawed}} = 11x + 500\]
According to the question,
\[
  \,\,\,\,\,\,\,\dfrac{{24x}}{{11x + 500}} = \dfrac{3}{2} \\
   \Rightarrow 2\left( {24x} \right) = 3\left( {11x + 500} \right) \\
   \Rightarrow 48x = 33x + 1500 \\
   \Rightarrow 15x = 1500 \\
   \Rightarrow x = 100 \\
\]
The original income of Salim is calculated as follows:
\[
  \,\,\,\,\,\,{\text{Original}}\,{\text{Income of Salim}} = 20\left( {100} \right) \\
   \Rightarrow {\text{Original}}\,{\text{Income of Salim}} = Rs.2000 \\
\]
The original income of Jawed is calculated as follows:
\[\
  \,\,\,\,\,\,{\text{Original}}\,{\text{Income of Jawed}} = 11\left( {100} \right) \\
   \Rightarrow {\text{Original}}\,{\text{Income of Jawed}} = Rs.1100 \\
\]

Thus, the original income of Salim is Rs. 2000 and original income of Jawed is Rs. 1100.

Note: To find the solution of a linear equation first, simplify both sides of the equation. Now, move the variable terms to one side and all other terms to another side. Then multiply or divide by the coefficient of the variable to find the solution of the given linear equation.