Question

c Present age of Amit and his father are in ratio 2 : 5 respectively. Four years hence the ratio of their ages becomes 5:11 respectively. What was the father's age five years ago? (A) 40 yrs (B) 45 yrs (C) 30 yrs (D) 35 yrs Space for Rough Work 2x + 5x ou​

Answer 1

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

Given that,

• Present age of Amit and his father are in the ratio 2 : 5.

So,

Let assume that

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Present \: age \: of \: Amit \: be \: 2x\: years} \\ \\ &\sf{Present \: age \: of \: Amit \: father \: be \: 5x \: years} \end{cases}\end{gathered}\end{gathered}$

So, After 4 years

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Age \: of \: Amit \: be \: 2x + 4\: years} \\ \\ &\sf{Age \: of \: Amit \: father \: be \: 5x + 4\: years} \end{cases}\end{gathered}\end{gathered}$

According to statement

$\rm :\longmapsto\:(2x + 4) : (5x + 4) = 5 : 11$

$\rm :\longmapsto\:\dfrac{2x + 4}{5x + 4} = \dfrac{5}{11}$

$\rm :\longmapsto\:5(5x + 4) = 11(2x + 4)$

$\rm :\longmapsto\:25x + 20= 22x + 44$

$\rm :\longmapsto\:25x - 22x = 44 - 20$

$\rm :\longmapsto\:3x = 24$

$\bf\implies \:x = 8$

Therefore,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Present \: age \: of \: Amit \: be \: 2 \times 8 = 16\: years} \\ \\ &\sf{Present \: age \: of \: Amit \: father \: be \: 5 \times 8 = 40 \: years} \end{cases}\end{gathered}\end{gathered}$

So, 5 years ago

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Age \: of \: Amit \: be \: 11\: years} \\ \\ &\sf{Age \: of \: Amit \: father \: be \: 35\: years} \end{cases}\end{gathered}\end{gathered}$

Hence, Option (d) is correct

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Basic Concept Used :-

Writing System 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.