Age Calculation Strategy
This problem involves setting up equations based on the relationships between Vanraj's, his son's, and his daughter's ages, both currently and in the past.
Defining Variables
- Let Vanraj's current age be V.
- Let his son's current age be S.
- Let his daughter's current age be D.
Formulating Equations
From the problem statement:
- Vanraj is three times as old as his son: $V = 3S$
- Daughter is 3 years younger than the son: $D = S - 3$
- The sum of their ages 3 years ago was 93: $(V - 3) + (S - 3) + (D - 3) = 93$
Solving the Age Equations
- Simplify the sum equation: $V + S + D - 9 = 93$ $V + S + D = 102$
- Substitute the expressions for $V$ and $D$ (in terms of $S$) into the simplified sum equation: $(3S) + S + (S - 3) = 102$
- Combine like terms: $5S - 3 = 102$
- Solve for the son's current age (S): $5S = 102 + 3$ $5S = 105$ $S = 105 / 5$ $S = 21$
- Calculate Vanraj's present age (V) using $V = 3S$: $V = 3 * 21$ $V = 63$
Conclusion
Vanraj's present age is 63 years.
Important Questions from Problem on Age
The ratio of present ages of A and B is 7 : 8. After 6 years from now, the ratio of their ages will be 8 : 9. If C's present age is 10 years more than the present age of A, then the present age (in years) of C is:
Three years ago, the ratio of the age of father to that of his son was 8 ∶ 3. After 4 years, their ages will be in the ratio 11 ∶ 5. What is the present age (in years) of the father?
At present, A is younger than B by 8 years. If 4 years ago, their ages were in the ratio 1 ∶ 2, then what is the present age of B (in years)?
Eight years ago, the ratio of ages of A and B was 5 ∶ 4. The ratio of their present ages is 6 ∶ 5. What will be the sum (in years) of the ages of A and B after 7 years from now?
Ratio of the present age of a mother to that of the daughter is 7 ∶ 1. After 5 years the ratio will become 4 ∶ 1. What is the difference (in years) in their present ages?
