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 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:
One year ago, the ratio of the ages of A and B was 4 : 3. The ratio of their ages, after 7 years from now, will be 9 : 7. What is the present age (in years) of B?
In 8 years, Subhash will be 3 times as old as he is now. After how many years will Subhash be 5 times as old as he is now?
The average ages of parents and two children are 30 years and 8 years respectively. The average age of the family is
A. 16 years
B. 19 years
C. 18 years
D. 17 years
A father is presently 3 times his daughter’s age. After 10 years he will be twice as old as her. Find the daughter’s present age.
