Age Ratio Calculation
Let the present ages of P and Q be represented using the variable $x$. According to the given ratio 3 : 4:
- Present age of P = $3x$
- Present age of Q = $4x$
After 6 years, their ages will increase by 6 years:
- P's age after 6 years = $3x + 6$
- Q's age after 6 years = $4x + 6$
The problem states that after 6 years, the ratio of their ages will be 4 : 5. We can write this as an equation:
$ \frac{3x + 6}{4x + 6} = \frac{4}{5} $
To solve for $x$, we cross-multiply:
$ 5 \times (3x + 6) = 4 \times (4x + 6) $
$ 15x + 30 = 16x + 24 $
Now, rearrange the terms to isolate $x$:
$ 30 - 24 = 16x - 15x $
$ 6 = x $
So, the value of $x$ is 6.
Determining P's Present Age
The question asks for the present age of P. P's present age is represented by $3x$. Substitute the value of $x = 6$:
P's present age = $3 \times 6 = 18$ years.
Important Questions from Problems on Age
- If 2 times a son's age is added to his father's age, the sum is 46 years. If 2.5 times the father's age is added to the son's age, the sum is 97 years. What is the father's age (in years)?
- If 2 times the age of Ram is 25 years more than 9 times the age of Ramya, and 5 times the age of Ramya is 4 years less than the age of Ram, then what is the difference (in years) between the ages of Ram and Ramya?
- The present ages of Sheo Kumar and Dileep Kumar are in the ratio of $9 : 10$. After $11\text{ years}$ this ratio will become $10 : 11$. What are the present ages of Sheo Kumar and Dileep Kumar?
- Ten years ago, X was 5 years old and his age was half of the age of Y. At that time, Z was 8 years younger than his brother P. Z was 18 years old at that time. What is the ratio of the respective ages of Z and P at present?
- 4 times the present age of P exceeds the present age of Q by 19 years. After 5 years, 3 times the age of Q will be 27 years less than 9 the age of P. The present age of Q is (in years):
