Age Ratio Calculation
Let the present ages of Ayushi and Anmol be $2x$ and $3x$ respectively, based on the given ratio $2 : 3$.
Future Age Ratio Equation
After 6 years, their ages will be $(2x + 6)$ for Ayushi and $(3x + 6)$ for Anmol. The ratio of their future ages is given as $8 : 9$. We can set up the equation:
$ \frac{2x + 6}{3x + 6} = \frac{8}{9} $
Solving for x
Cross-multiply to solve the equation:
$ 9(2x + 6) = 8(3x + 6) $
$ 18x + 54 = 24x + 48 $
Rearrange the terms to find $x$:
$ 54 - 48 = 24x - 18x $
$ 6 = 6x $
$ x = 1 $
Finding Present Ages and Difference
Now, calculate their present ages using $x=1$:
- Ayushi's present age = $2x = 2(1) = 2$ years.
- Anmol's present age = $3x = 3(1) = 3$ years.
The positive difference in their present ages is:
$ \text{Difference} = 3 - 2 = 1 \text{ year} $
Important Questions from Problem on Age
The ratio of present ages of A and B is 7 : 8. After 6 years from now, the ratio of their ages will be 8 : 9. If C's present age is 10 years more than the present age of A, then the present age (in years) of C is:
Three years ago, the ratio of the age of father to that of his son was 8 ∶ 3. After 4 years, their ages will be in the ratio 11 ∶ 5. What is the present age (in years) of the father?
At present, A is younger than B by 8 years. If 4 years ago, their ages were in the ratio 1 ∶ 2, then what is the present age of B (in years)?
Eight years ago, the ratio of ages of A and B was 5 ∶ 4. The ratio of their present ages is 6 ∶ 5. What will be the sum (in years) of the ages of A and B after 7 years from now?
Ratio of the present age of a mother to that of the daughter is 7 ∶ 1. After 5 years the ratio will become 4 ∶ 1. What is the difference (in years) in their present ages?
