6. The present ages of A and B are 23 years and 31years respectively.

1.	6. The present ages of A and B are 23 years and 31years respectively. After how many years the ratiobetween their ages will be 11 : 13?is
Answer» ${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$ Given: Present age of A = 23years Present age of B = 31 years $\\$ To FIND: The NUMBER of years after which the ratio between their ages will be 11:13 $\\$ Assumption: Let the number of years be x. $\\$ Solution: So, ⇒ Age of A after x years = (23 + x) years ⇒ Age of B after x years = (31 + x) years Hence, $\implies (23 + x) : (31 + x) = 11 : 13 \\\implies \dfrac{23 + x}{31 + x} = \dfrac{11}{13}$ On Cross- Multiplying, ⇒ (13)(23 + x) = (11)(31 + x) ⇒ 299 + 13x = 341 + 11x ⇒ 13x - 11x = 341 - 299 ⇒ 2x = 42 ⇒ x = 21 So, after 21 years the ratio between the ages of A and B will be 11:13. $\\$ Verification: ⇒ Age of A after x years = (23 + x) years = 23 + 21 = 44 years ⇒ Age of B after x years = (31 + x) years = 31 + 21 = 52 years ⇒ Ratio of ages of A and B = 44:52 On dividing by 4, ⇒ Ratio of ages of A and B = 11 : 13 Hence verified too!

6. The present ages of A and B are 23 years and 31years respectively. After how many years the ratiobetween their ages will be 11 : 13?is

Answer»

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

Given:

Present age of A = 23years
Present age of B = 31 years

$\\$

To FIND:

The NUMBER of years after which the ratio between their ages will be 11:13

$\\$

Assumption:

Let the number of years be x.

$\\$

Solution:

So,

⇒ Age of A after x years = (23 + x) years

⇒ Age of B after x years = (31 + x) years

Hence,

$\implies (23 + x) : (31 + x) = 11 : 13 \\\implies \dfrac{23 + x}{31 + x} = \dfrac{11}{13}$

On Cross- Multiplying,

⇒ (13)*(23 + x) = (11)*(31 + x)

⇒ 299 + 13x = 341 + 11x

⇒ 13x - 11x = 341 - 299

⇒ 2x = 42

⇒ x = 21

So, after 21 years the ratio between the ages of A and B will be 11:13.

$\\$

Verification:

⇒ Age of A after x years = (23 + x) years = 23 + 21 = 44 years

⇒ Age of B after x years = (31 + x) years = 31 + 21 = 52 years

⇒ Ratio of ages of A and B = 44:52

On dividing by 4,

⇒ Ratio of ages of A and B = 11 : 13

Hence verified too!