Question

two years ago Deepika age was 8 times divyas age after 1 year Deepika age will be 5 times Divya age so find out the age of both​

Answer 1

Answer:

Age of Deepika is 34 years and age of Divya is 6 years

Step-by-step explanation:

Let present age of Deepika be $x$ years

Let present age of Divya be $y$ years

Two years ago,

Age of Deepika $=x - 2$ years

Age of Divya $=y - 2$ years

Given that 2 years ago, deepika's age was 8 times divya's age

We have

$x - 2 = 8 \times (\,y - 2)\,\\\\x - 2 = 8y - 16\\\\x - 8y = -14 ----- (1)$

1 years after,

Age of Deepika $=x + 1$ years

Age of Divya $=y + 1$ years

Given that 1 year after, deepika's age was 5 times divya's age

We have

$x + 1 = 5 \times (\,y + 1)\,\\\\x + 1 = 5y + 5\\\\x - 5y = 4 ----- (2)$

Solving (1) and (2)

 x - 8y = -14

 x - 5y = 4

(-)  (+)     (-)

----------------------

    -3y = -18

       y = $\frac{-18}{-3}$

       y = 6

Putting valye of y in (2), we get

$x - 5(\,6)\, = 4\\\\x - 30 = 4\\\\x = 34$

Thus, age of Deepika is 34 years and age of Divya is 6 years