Ratio of P and Q Ages
The problem states that the ages of two individuals, P and Q, are in the ratio $5:9$. This means that for every 5 units of P's age, Q's age is 9 units. We can represent their ages using a common multiplier, let's call it '$x$'.
- P's age = $5x$
- Q's age = $9x$
Determine P's Age Factor
We are given that P's actual age is $25$ years. We can use this information to find the value of the multiplier '$x$'.
Set P's age in terms of '$x$' equal to the given age:
$5x = 25$
To find '$x$', divide both sides of the equation by 5:
$x = \frac{25}{5}$
$x = 5$
So, the common multiplier '$x$' is 5.
Calculate Q's Actual Age
Now that we know '$x = 5$', we can calculate Q's actual age using the representation from the first step:
Q's age = $9x$
Substitute the value of '$x$':
Q's age = $9 \times 5$
Q's age = $45$ years
Find Age Difference: Q minus P
The question asks how many years older Q is than P. To find this, we need to calculate the difference between Q's age and P's age.
- Q's age = $45$ years
- P's age = $25$ years
Age difference = Q's age - P's age
Age difference = $45 - 25$
Age difference = $20$ years
Therefore, Q is $20$ years older than P.
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:
