Question

the ages of two persons are in the ratio of 5:7 eighteen years ago their ages were in the ratio of 8:13 their present ages are ?​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Their present age is 50 and 70 years.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

The ratio of present ages = 5 : 7

Eighteen years ago = 8 : 13

To find :

Their present ages

Solution :

Consider the present ages as 5x and 7x

$\sf{ \dfrac{5x - 18}{7x - 18} = \dfrac{8}{13}}$

$\implies$ 13(5x - 18) = 8(7x - 18)

$\implies$ 65x - 234 = 56x - 144

$\implies$ 65x - 56x = - 144 + 234

$\implies$ 9x = 90

$\implies$ x = 90/9

$\implies$ x = 10

$\rule{300}{1}$

Value of 5x

$\implies$ 10 × 5

$\implies$ 50

Value of 7x

$\implies$ 7 × 10

$\implies$ 70

$\therefore$ Their present age is 50 and 70 years.

$\rule{300}{1}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\implies$ 13(50 - 18) = 8(70 - 18)

$\implies$ 650 - 234 = 560 - 144

$\implies$ 650 - 560 = - 144 + 234

$\implies$ 90 = 90

$\therefore$ Their present age is 50 and 70 years.

Answer 2

Answer:

LINEAR EQUATIONS IN TWO VARIABLES :

Let the present age of Person 1 be x years and the another be y years .

Then, $\mathsf{\dfrac{x}{y}}$ = $\mathsf{\dfrac{5}{7}}$

7x = 5y

7x - 5y = 0

x = 5y/ 7 --> ( 1 )

Now, 18 years ago,

Age of 1st Person = ( x - 18 ) years

Age of 2nd Person = ( y - 18 ) years.

According to the question,

$\mathsf{\dfrac{(x\:-\:18)}{(y\:-\:18}}$ = $\mathsf{\dfrac{8}{13}}$

13( x - 18 ) = 8( y - 18 )

13x - 234 = 8y - 144

13x - 8y = 234 - 144

13x - 8y = 90 --> ( 2 )

Putting value of ' x ' in equation ( 2 ),

$\mathsf{\dfrac{13*5y}{7} \:-\:8y\:=\:90}$

65y - 56y = 630

9y = 630

y = 630/9

y = 70

Putting value of ' y ' in equation ( 1 ),

x = 5y/7

x = 5 * 70/ 7

x = 50

⛛ The present ages of two persons are 50 and 70 years respectively.