Question

ratan is 12 years older than reema .after 4 years ratans age will be equal to thrice the age of reema. find their present age​

Answer 1

Present age of Ratan = 14 years and present age of Reema = 2 years

Given :

• Ratan is 12 years older than Reema

• After 4 years Ratan's age will be equal to thrice the age of Reema

To find :

Present age of Ratan and Reema

Solution :

Step 1 of 2 :

Form the equation to calculate present age of Ratan and Reema

Let present age of Reema = x years

Since Ratan is 12 years older than Reema

∴ Present age of Ratan = (x + 12) years

After 4 years

Age of Reema = (x + 4) years

Age of Ratan = (x + 12 + 4) years = (x + 16) years

Since after 4 years Ratan's age will be equal to thrice the age of Reema

By the given condition

$\displaystyle \sf (x + 16) = 3(x + 4)$

Step 2 of 2 :

Calculate present age of Ratan and Reema

$\displaystyle \sf (x + 16) = 3(x + 4)$

$\displaystyle \sf{ \implies }x + 16 = 3x + 12$

$\displaystyle \sf{ \implies }3x + 12 = x + 16$

$\displaystyle \sf{ \implies }3x - x = 16 - 12$

$\displaystyle \sf{ \implies }2x = 4$

$\displaystyle \sf{ \implies }x = \frac{4}{2}$

$\displaystyle \sf{ \implies }x = 2$

Present age of Reema = x years = 2 years

Present age of Ratan

= (x + 12) years

= (2 + 12) years

= 14 years

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Answer 2

Reema's present age is 2 years and Ratan's present age is 14 years.

Let, Reema's present age be 'x' years.

Ratan's present age = (x + 12) years.

After 4 years,

Reema's age = (x + 4) years

Ratan's age = (x + 12 + 4) = (x + 16) years

According to the question,

Ratan's age = 3 ( Reema's age)

$(x + 16) = 3 (x + 4)\\x + 16 = 3x + 12\\2x = 4\\x = 2$

Therefore, Reema's present age is 2 years.

and Ratan's present age = (x + 12) = (2 + 12) = 14 years.

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