Question

Question.15: Five years ago, Anu was thrice as old as Sonu. After ten years, Anu will be twice as old as Sonu. How old are Anu and Sonu?

Answer 1

Answer:

Let us assume the present ages of Anu is x and Sonu is y.

According to the question:

x – 5 = 3(y – 5)

x – 5 = 3y – 15

x= 3y-15+5

x= 3y -10……………….. (1)

Again, as per question;

x + 10 = 2(y + 10)

x + 10 = 2y + 20

x – 2y = 10

(3y – 10) – 2y = 10 (from equation 1)

3y-2y =10+10

y= 20

Substitute, y=20 in equation 1,

x = 3(20) -20

x =60 – 20

x = 50

Hence, the present ages of Anu is 50 years and of Sonu is 20 years.

Step-by-step explanation:

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Answer 2

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

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

According to statement,

$\begin{gathered}\begin{gathered}\bf\: 5 \: years \: ago-\begin{cases} &\sf{age \: of \: Anu = x - 5 \: years} \\ &\sf{age \: of \: Sonu = y - 5 \: years} \end{cases}\end{gathered}\end{gathered}$

☆ Anu was thrice as old as Sonu

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

$\rm :\longmapsto\:x - 5 = 3y - 15$

$\red{\rm :\longmapsto\:x - 3y = - 10 - - - (1)}$

According to statement again,

$\begin{gathered}\begin{gathered}\bf\: 10 \: years \: after-\begin{cases} &\sf{age \: of \: Anu = x + 10 \: years} \\ &\sf{age \: of \: Sonu = y + 10\: years} \end{cases}\end{gathered}\end{gathered}$

☆ Anu will be twice as old as Sonu.

$\rm :\longmapsto\:x + 10 = 2(y + 10)$

$\rm :\longmapsto\:x + 10 = 2y + 20$

$\red{\rm :\longmapsto\:x - 2y = 10 - - - (2)}$

On Subtracting equation (1) from equation (2), we get

$\rm :\longmapsto\:y = 20 - - - - (3)$

On substituting the value of y in equation (2), we get

$\rm :\longmapsto\:x - 2 \times 20 = 10$

$\rm :\longmapsto\:x - 40 = 10$

$\bf\implies \:x = 50$

$\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{present \: age \: of \: Anu = 50 \: years} \\ &\sf{present \: age \: of \: Sonu = 20 \: years} \end{cases}\end{gathered}\end{gathered}$

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.