To find the present age of Q, we need to first use the given conditions and form equations. Let's denote the present ages of P and Q as \( p \) and \( q \) respectively.
- According to the first condition: "Five times the present age of P exceeds the present age of Q by 29 years."
- This can be formulated as: 5p = q + 29
- The second condition states: "After 8 years, five times Q's age will be 17 years less than seven times P's age at that time."
- In 8 years, the ages of P and Q will be \( p + 8 \) and \( q + 8 \) respectively.
- The condition becomes: 5(q + 8) = 7(p + 8) - 17
Next, we'll solve these equations step-by-step:
- Simplify the equation from step 2:
- 5q + 40 = 7p + 56 - 17
- Rearranging gives: 5q + 40 = 7p + 39
- Simplify further to: 5q = 7p - 1
- We now have two equations:
- \(5p = q + 29\)
- \(5q = 7p - 1\)
- Substitute \( q = 5p - 29 \) from the first equation into the second:
- 5(5p - 29) = 7p - 1
- Expanding: 25p - 145 = 7p - 1
- Further simplify: 25p - 7p = 145 - 1
- \(18p = 144\)
- \(p = \frac{144}{18} = 8\)
- Now find \( q \) using \( q = 5p - 29 \):
- \(q = 5 \times 8 - 29\)
- \(q = 40 - 29 = 11\)
Thus, the present age of Q is 11 years.
This matches with the correct option, which is 11.
Important Questions from Age
- 7 years ago, the age of a father was 13 years more than twice his son's age. After how many years, from now, will he be twice his son's age?
If 2 times the mother's age is 26 years more than 4 times her daughter's age, and 3 times the daughter's age is 7 years less than the mother's age, then what is the difference (in years) between the ages of the mother and the daughter?
If 2 times a son's age is added to his father's age, the sum is 36 years. If 2.5 times the father's age is added to the son's age, the sum is 72 years. What is the father's age (in years)?
- Six times the present age of P exceeds the present age of Q by 11 years. After 10 years, three times Q's age will be 27 years less than six times P's age at that time. What is the present age (in years) of Q?
Two times the present age of P exceeds the present age of Q by 41 years. After 7 years, nine times Q's age will be 24 years less than six times P's age at that time. What is the present age (in years) of Q?
