Question

The present age of Aman is twice that of Raj. The sum of their present ages is 33 years. Find the present age of Aman (in years).​

Answer 1

Let,

• The present age of Raj be x yrs
• Then,the age of Aman will be 2x yrs.

A/Q,

x + 2x = 33

⇝ 3x = 33

⇝ x = 33/3

⇝ x = 11

Verification:

LHS = x + 2x = 11 + 2(11 ) = 11 + 22 = 33

RHS = 33

33 = 33

LHS = RHS

Hence,verified!!

Therefore,

• Present age of Raj = x = 11yrs
• Present age of Aman = 2x = 2 × 11 = 22

Hence, the present age of Aman is 22yrs

Answer 2

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

Given that

↝ The present age of Aman is twice that of Raj.

Let assume that Raj present age be 'x' years.

So,

Aman present age be '2x' years.

So, we have

$\red{\begin{gathered}\begin{gathered}\bf\: Present \: age \: of \: \begin{cases} &\sf{Raj = x \: years} \\ \\ &\sf{Aman = 2x \: years} \end{cases}\end{gathered}\end{gathered}}$

Now, Further given that

↝ The sum of their present ages is 33 years

$\rm \implies\:x + 2x = 33$

$\rm \implies\:3x = 33$

$\rm \implies\: \: \boxed{ \tt{ \: x = 11 \: }}$

Hence,

$\red{\begin{gathered}\begin{gathered}\bf\: Present \: age \: of \: \begin{cases} &\sf{Raj = 11 \: years} \\ \\ &\sf{Aman = 2 \times 11 = 22 \: years} \end{cases}\end{gathered}\end{gathered}}$

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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.