Question

The ages of Hari and Harry are in ratio5:7.four years from now the ratio of their ages will be 3:4.find their
present ages.

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

The ages of Hari and Harry are in ratio 5:7 . After four years , now the ratio of their ages will be 3:4 . find their present ages.

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{Given}}}}$

• The ages of Hari and Harry are in ratio 5:7
• After four years now the ratio of their ages will be 3:4 .

$\Large{\underline{\mathfrak{\bf{Find}}}}$

• Present ages of Hari and Harry

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

Let,

• Age of Hari = x years
• Age of Harry = y years

A/c to question ,

( The ages of Hari and Harry are in ratio 5:7 )

$\mapsto\sf{\:\dfrac{x}{y}\:=\:\dfrac{5}{7}} \\ \\ \mapsto\sf{\:7x\:-5y\:=\:0.........(1)}$

Again,

( After four years now the ratio of their ages will be 3:4 )

$\mapsto\sf{\:\dfrac{x+4}{y+4}\:=\:\dfrac{3}{4}} \\ \\ \mapsto\sf{\:4(x+4)\:=\:3(y+4)} \\ \\ \mapsto\sf{\:4x\:-\:3y\:=\:12\:-\:16} \\ \\ \mapsto\sf{\:4x\:-\:3y\:=\:-4.......(2)}$

multiply by 4 in equ(1) and 7 in equ(2)

• 28x - 20y = 0
• 28x - 21y = - 28

Subtract this,

$\mapsto\boxed{\sf{\:y\:=\:28}}$

keep value in equ(1) ,

$\mapsto\sf{\:7x\:-5\times 28\:=\:0} \\ \\ \mapsto\sf{\:7x\:=\:140} \\ \\ \mapsto\sf{\:x\:=\:\dfrac{140}{7}} \\ \\ \mapsto\boxed{\sf{\:x\:=\:20}}$

$\Large{\underline{\mathfrak{\bf{Thus}}}}$

• Age of Hari (x) = 20 years
• Age of Harry (y) = 28 years

Answer 2

Present age of Hari is 20 years

Present age of Harry is 28 years.

Step-by-step explanation:

Let the Present age of Hari be $x$ years

and the Present age of Harry be $y$ years.

• First condition states that the ages of Hari and Harry are in ratio 5 : 7, that means;

                                 $\frac{x}{y} = \frac{5}{7}$

                                 $x=\frac{5y}{7}$  ---------------- [Equation 1]

• Second condition states that four years from now the ratio of their ages will be 3 : 4, that means;

                         

                                   $\frac{x+4}{y+4} =\frac{3}{4}$

                            $4(x+4) =3(y+4)$  

                             $4x+16=3y+12$

                             $4x-3y=12-16$

                              $4x-3y=-4$

Now, putting value of $x$ from equation 1 into the above equation, we get;

                              $4 \times \frac{5y}{7} -3y = -4$

                               $\frac{20y}{7} -3y = -4$

                                $\frac{20y-21y}{7} = -4$

                                   $\frac{-y}{7} = -4$

                                    $y=7 \times 4$ = 28 years

So, putting value of $y$ in equation 1, we get;

                         $x=\frac{5\times 28}{7}$

                        $x={5\times 4}$ = 20 years

Hence, Present age of Hari is 20 years and Present age of Harry is 28 years.