QB_PH_GA_015: Quantitative Aptitude

The ratio of the present ages of a father and his son is $7 : 3$. Four years ago, the ratio of their ages was $3 : 1$. What is the present age of the father in years?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Linear Variable Assignment**: Let present ages be $7x$ (father) and $3x$ (son). 2. **Condition 4 Years Ago**: $\frac{7x - 4}{3x - 4} = \frac{3}{1}$ 3. **Cross-Multiplication**: $7x - 4 = 3(3x - 4)$ $7x - 4 = 9x - 12$ $9x - 7x = 12 - 4 \implies 2x = 8 \implies x = 4$ 4. **Present Age of Father**: $\text{Age} = 7x = 7 \times 4 = 28\text{ years}$ (Son's present age $= 3 \times 4 = 12\text{ years}$; four years ago: $24$ and $8$, ratio $= 24/8 = 3/1$). 5. **Official Value**: 28.