Age Ratio Calculation: Finding Present Ages
The problem asks for the current ages of A and B given their age ratio and the sum of their ages after a decade.
Representing Present Ages
- Let the present age of A be $3x$ years.
- Let the present age of B be $2x$ years.
- The ratio A:B is currently $3x : 2x$, which simplifies to $3:2$.
Calculating Future Ages
In 10 years:
- A's age will be $3x + 10$.
- B's age will be $2x + 10$.
Using the Sum of Future Ages
We are given that the sum of their ages after 10 years will be 80.
Therefore, the equation is:
$ (3x + 10) + (2x + 10) = 80 $Solving for x
- Combine like terms: $5x + 20 = 80$.
- Subtract 20 from both sides: $5x = 80 - 20$.
- Simplify: $5x = 60$.
- Divide by 5: $x = \frac{60}{5}$.
- Calculate the value of x: $x = 12$.
Determining Present Ages
Now substitute the value of $x$ back into the expressions for their present ages:
- A's present age = $3x = 3 \times 12 = 36$ years.
- B's present age = $2x = 2 \times 12 = 24$ years.
The respective present ages of A and B are 36 and 24 years.
Important Questions from Age
The ratio of the ages of A and B, four years ago, was 4 : 5. Eight years from now, the ratio of the ages of A and B will be 11 : 13. What is the sum of their present ages?
The ratio of the present ages of A and B is 8 : 9. After 9 years, this ratio will become 19 : 21. C is 3 years younger to B. What is the present (in years) of C?
The ratio of the ages of A and B 8 years ago was 2 : 3. Four years ago, the ratio of their ages was 5 : 7. What will be the ratio of their ages 8 years from now?
The ratio of the present age of father to that of his son is 7 : 2. If after 10 years the ratio of their ages will become 9 : 4, then the present age of the father is:
The ages of two persons P and Q are in the ratio 5 : 7. Eight years ago, the ratio of P and Q was 7 : 13. The present ages of P and Q, respectively, are:
