Question

6.
Two years ago, Dilip was three times as old as his son and two years
hence, twice his age will be equal to five times that of his son.
Find
their present ages.
(Ans : 14 years, 38 years)​

Answer 1

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.

Let's solve the problem now!!!

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

$\begin{gathered}\begin{gathered}\bf\: Let-\begin{cases} &\sf{present \: age \: of \: Dilip = x \: years} \\ &\sf{present \: age \: of \: Son \: = y \: years} \end{cases}\end{gathered}\end{gathered}$

Now,

Two years ago,

$\begin{gathered}\begin{gathered}\bf\: Age \: of-\begin{cases} &\sf{Dilip = x - 2 \: years} \\ &\sf{Son \: = y - 2 \: years} \end{cases}\end{gathered}\end{gathered}$

According to statement

Age of Dilip is 3 times the age of his son.

$\rm :\longmapsto\:x - 2 = 3(y - 2)$

$\rm :\longmapsto\:x - 2 = 3y - 6$

$\bf\implies \:\:x = 3y - 4 - - - (1)$

Now,

After 2 years,

$\begin{gathered}\begin{gathered}\bf\: Age \: of-\begin{cases} &\sf{Dilip = x + 2 \: years} \\ &\sf{Son \: = y + 2 \: years} \end{cases}\end{gathered}\end{gathered}$

According to statement

Twice the age of Dilip will be equal to five times of his son.

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

$\rm :\longmapsto\:2(3y - 4 + 2) = 5(y + 2) \: \: \: \: \{ \: using \: (1) \}$

$\rm :\longmapsto\:2(3y - 2) = 5(y + 2)$

$\rm :\longmapsto\:6y -4= 5y + 10$

$\rm :\longmapsto\:6y - 5y = 10 + 4$

$\rm :\implies\:\purple{\boxed{ \bf \: y = 14}}$

Put y = 14 in equation (1), we get

$\rm :\longmapsto\:x = 3 \times 14 - 4$

$\rm :\longmapsto\:x = 42 - 4$

$\rm :\implies\:\purple{\boxed{ \bf \: x = 38}}$

$\pink{\begin{gathered}\begin{gathered}\bf\: Hence-\begin{cases} &\sf{present \: age \: of \: Dilip = 38 \: years} \\ &\sf{present \: age \: of \: Son \: = 14 \: years} \end{cases}\end{gathered}\end{gathered}}$