Ram's son's age is $\frac{1}{3}$ of Ram's wife's age. Ram's wife's age is $\frac{4}{5}$ of Ram's age and Ram's age is $\frac{3}{5}$ of Ram's father's age. Find the age of Ram's son, if Ram's father is 50 years old.

### Concept & Logic This problem is a sequential chain of fractional dependencies. To solve it efficiently, start from the single absolute numerical value provided at the end of the chain and calculate backwards step-by-step. ### Step-by-Step Solution * **Given:** * Son = $\frac{1}{3} \times$ Wife * Wife = $\frac{4}{5} \times$ Ram * Ram = $\frac{3}{5} \times$ Father * Father = $50$ years * **Calculation / Deduction:** * First, calculate Ram's actual age using his father's age: * Ram = $\frac{3}{5} \times 50 = 3 \times 10 = 30$ years. * Next, calculate Ram's wife's age using Ram's age: * Wife = $\frac{4}{5} \times 30 = 4 \times 6 = 24$ years. * Finally, calculate Ram's son's age using his wife's age: * Son = $\frac{1}{3} \times 24 = 8$ years. ### Exam Strategy & Shortcut You can combine all the fractions into a single, continuous multiplication chain in one line to completely eliminate intermediate calculations and save writing time: Son's Age = $\frac{1}{3} \times \frac{4}{5} \times \frac{3}{5} \times 50$ $= \frac{12}{75} \times 50$ $= 12 \times \frac{2}{3} = 8$ years. ### Common Pitfall Getting disorganized and misreading the chain of relationships, which often leads to multiplying the fractions in the wrong order or accidentally skipping an entire generation in the sequence. ### Final Answer **Therefore, the correct answer is 8 years.**