Question

The present age of Ankur And Aryan are in the ratio 1: 2 .Three years from now the ratio of their age will be 3 :5 ,Find their present age​

Answer 1

Answer:

Present age of Ankur = x = 6 years

Present age of Aryan = 2x = 2 × 6 = 12 years

Step-by-step explanation:

$\red{ \underline{ \frak{Given}}:-}$

The present age of Ankur apnd Aryan are in the ratio 1:2 .Three years from now the ratio of their age will be 3:5

$\red{ \underline{ \frak{To \: Find:-}}}$

Their present ages

$\red{ \underline{ \frak{Solution:-}}}$

$\rm \purple{Let}$ :-

• The present age of Ankur and Aryan be x and 2x years respectively

${ \huge \:{ ♦}} \: \rm After \: 3 \: years$

• Ankur's age will be x + 3 years
• Aryan's age = 2x + 3 years

So,

ACQ

$\therefore \ \: \rm \bigg \{\frac{x + 3}{2x + 3} \bigg \} = \frac{3}{5} \\ \\ \sf \: by \: cross \: multiplying \\ \\ \tt 5(x + 3) = 3(2x + 3) \\ \\ \tt \: 5x + 15 = 6x + 9 \\ \\ \tt 5x - 6x = 9 - 15 \\ \\ \tt \: \cancel- x = \cancel - 6 \\ \\ \maltese \boxed{\purple{ \bf \: x = 6}}$

So,

Present age of Ankur = x = 6 years

Present age of Aryan = 2x = 2 × 6 = 12 years

V E R I F I C A T I O N :-

Ratio between Ankur and Aryan = 6 : 12 = 1:2

This step is correct ✓

Next Step

After 3 years

Ankur's age = 6 + 3 = 9 years

Aryan's age = 12 + 3 = 15 years

Required ratio = 9:15 = 3:5

It is also correct ✓. So, our answer is correct

Hence Verified

MORE TO KNOW -

Definition of Equation

→ A statement of equality which contains one or more unknown quantity or variable (literals) is called an equation.

Definition of Linear Equation

→ An equation involving only linear polynomials is called a linear equation

Definition of Solution of a Linear Equation

→ A value of the variable which when substituted for the variable in an equation, makes LHS = RHS is said to satisfy the equation and is called a salution or root of the equation

________________________

Answer 2

$\sf\small\underline\green{Let:-}$

$\tt{:\implies The\: present\:age\:_{(Ankur)}=x}$

$\tt{:\implies The\: present\:age\:_{(Aryan)}=y}$

$\sf\small\underline\green{To\: Find:-}$

$\tt{:\implies The\: present\:age\:_{(Their)}=?}$

$\sf\small\underline\green{Solution:-}$

To calculate the present age of Ankur and Aryan , at 1st we have to set up equation as per the given clue in the question. Then solve the equation to find out the age of Ankur and Aryan.

$\sf\small\underline{Given\:in\:case-(i):-}$

$\tt{:\implies Ankur\:age\:: Aryan\:age=1:2}$

$\tt{:\implies x:y=1:2}$

$\tt{:\implies 2x=y-------(i)}$

$\sf\small\underline{Given\:in\:case-(i):-}$

$\tt{:\implies After\:3\: years\:_{(Ankur\:age: Aryan\:age)}=3:5}$

$\tt{:\implies (x+3):(y+3)=3:5}$

$\tt{:\implies 5(x+3)=3(y+3)}$

$\tt{:\implies 5x+15=3y+9}$

$\tt{:\implies 5x-3y=9-15}$

$\tt{:\implies 5x-3y=-6----(ii)}$

• Substitutes the value y in eq (ii)

$\tt{:\implies 5x - 3(2x)=-6}$

$\tt{:\implies 5x-6x=-6}$

$\tt{:\implies -x=-6}$

$\tt{:\implies x=6}$

• Putting the value of x in eq (ii)

$\tt{:\implies 5x-3y=-6}$

$\tt{:\implies 5(6)-3y=-6}$

$\tt{:\implies 30-3y=-6}$

$\tt{:\implies -3y=-6-30}$

$\tt{:\implies 3y=36}$

$\tt{:\implies y=12}$

$\sf\large{Hence,}$

$\tt\blue{:\implies The\: present\:age\:_{(Ankur)}=6\: years}$

$\tt\green{:\implies The\: present\:age\:_{(Aryan)}=12\: years}$