Question

the ratio of the present age of a brother and sister is 7:4. four years ago the ratio of their ages was 5:2.find their present age​
answer this question with photo plz

Answer 1

$\large\underline{\bf{Solution-}}$

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{present \: age \: of \: Brother = 7x \: years} \\ &\sf{present \: age \: of \: Sister = 4x \: years} \end{cases}\end{gathered}\end{gathered}$

Four years ago

$\begin{gathered}\begin{gathered}\bf\: Age \: of-\begin{cases} &\sf{Brother = 7x - 4} \\ &\sf{Sister = 4x - 4} \end{cases}\end{gathered}\end{gathered}$

According to statement,

Four years ago, the ratio of their ages was 5 : 2.

$\rm :\longmapsto\:\dfrac{7x - 4}{4x - 4} = \dfrac{5}{2}$

$\rm :\longmapsto\:14x - 8 = 20x - 20$

$\rm :\longmapsto\:20x - 14x = 20 - 8$

$\rm :\longmapsto\:6x = 12$

$\bf\implies \:x = 2$

$\begin{gathered}\begin{gathered}\bf\: Hence-\begin{cases} &\sf{present \: age \: of \: Brother = 7 \times 2 = 14 \: years} \\ &\sf{present \: age \: of \: Sister = 4 \times 2 = 8 \: years} \end{cases}\end{gathered}\end{gathered}$

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.