Question

The sum of the ages of meena and rekha is 31 years .After 10 years the ratio of their ages will be 8:9 find their present ages

Answer 1

Answer:

MEENA'S AGE =14 AND REKHA'S AGE =16

Step-by-step explanation:

Let meen's present age be 'x' and rekha's present age 'y'

Hence x+y=31

i.e y=31-x

so after 10 year meena's age will be 'x+10'

and rekha's age will be 'y+10'

so $\frac{x+10}{y+10} =\frac{8}{9}$

so x=14 and y=16

Answer 2

Answer:

$x$ = 14 and $y$ = 17

Step-by-step explanation:

Let Meena's age be $x$ and Rekha's age be $y$
Sum of the ages of Meena and Rekha is 31 yrs.
∴ As per first condition,
$x$ + $y$ = 31 ···(1)
Now, after 10 years Meena's age will be $x + 10$ years
and Seema's will be $y + 10$ years and ratio will be 8:9
∴ According to second condition,
$\frac{x + 10}{y + 10}= \frac{8}{9}$
∴ By cross multiplication,
$9(x +10) = 8 (y + 10)$
∴ 9$x$ + 90 = 8$y$ + 80
∴ 9$x$ - 8$y$ = -90 + 80
∴ 9$x$ - 8$y$ = -10 ···(2)
Now multiplying eq. (1) by 8 we get.
$8x + 8y = 248$ ···(3)
∴Adding (2) and (3) we get,

${ {{8x - 8y =248} \atop {9x - 8y= -10}} \right.$
_______
$17x$      $= 238$
∴ $x = \frac{238}{17}$
∴$x$ = 14
Substituting $x= 14$ in eq. (1) we get,
14 + $y$ = 31
∴ 31- 14 = $y$
∴$17 = y$
∴ Meena's age = $x$ = 14
∴ Rekha's age = $y$ = 17