Question

The present age of a man is twice that of his son. Ten years hence their ages will be in the ratio 8:5. Find the present age of his son.​

Answer 1

Solution:

➡ Let the present age of the son be x years.

➡ Then, the present age of the father is 2x years.

Ten years hence,

➡ Age of son will be (x + 10) years

➡ Age of father will be (2x + 10) years

From the question,

$\sf\large\bf{\frac{2x + 10}{x + 10} = \frac{8}{5}}$

$\sf\to{5(2x + 10) = 8(x + 10)}$

$\sf \to{10x + 50 = 8x + 80}$

$\sf \to{10x - 8x = 80 - 50}$

$\sf \to{2x = 30}$

$\sf\to{x=\cancel\frac{30}{2}}$

$\sf \large\to{x\frak{= 15}}$

Hence, the present age of the son is 15 years

Answer 2

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

Given that,

↝ The present age of a man is twice that of his son.

Let assume that

Present age of son be 'x' years.

So,

Present age of Father '2x' years.

So, we have

$\purple{\begin{gathered}\begin{gathered}\bf\:\rm :\longmapsto\:Present \: age \: of \: \begin{cases} &\sf{Son = x \: years} \\ \\ &\sf{Man = 2x \:years } \end{cases}\end{gathered}\end{gathered}}$

Further given that,

↝ Ten years hence their ages will be in the ratio 8:5.

So, After 10 years

$\purple{\begin{gathered}\begin{gathered}\bf\:\rm :\longmapsto\:Age \: of \: \begin{cases} &\sf{Son = x + 10 \: years} \\ \\ &\sf{Man = 2x + 10 \:years } \end{cases}\end{gathered}\end{gathered}}$

According to statement

$\rm :\longmapsto\:\dfrac{2x + 10}{x + 10} = \dfrac{8}{5}$

$\rm :\longmapsto\:10x + 50 = 8x + 80$

$\rm :\longmapsto\:10x - 8x = 80 - 50$

$\rm :\longmapsto\:2x = 30$

$\rm \implies\:\boxed{ \tt{ \: x \: = \: 15 \: }}$

Hence,

$\purple{\begin{gathered}\begin{gathered}\bf\:\rm :\longmapsto\:Present \: age \: of \: \begin{cases} &\sf{Son = 15 \: years} \\ \\ &\sf{Man = 2 \times 15 = 30 \:years } \end{cases}\end{gathered}\end{gathered}}$

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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.