Ratio between the ages of Subhash, Prasad and Amar is $3 : 6 : 7$. If the difference between the ages of Prasad and Amar is 10 years, then what is the difference between the ages of Subhash and Prasad?

### Concept & Logic Treat ratio numbers as distinct, uniform building blocks (units). The true numerical difference between any two individuals' ages corresponds perfectly to the difference in their respective ratio units. ### Step-by-Step Solution * **Given:** * Subhash : Prasad : Amar = $3 : 6 : 7$ * Age difference (Prasad and Amar) = $10$ years * **Calculation / Deduction:** * Let their actual ages be $3x$, $6x$, and $7x$ respectively. * The difference between Prasad and Amar's ages algebraically is: * $7x - 6x = x$ * We are explicitly given that this difference is $10$ years, making $x = 10$. * The question asks for the difference between Subhash and Prasad's ages: * Difference = $6x - 3x = 3x$ * Substitute the known value of $x$: * Difference = $3 \times 10 = 30$ years. ### Exam Strategy & Shortcut Solve entirely in ratio units without deploying variables. Look at Prasad ($6$) and Amar ($7$). They have a gap of exactly $1$ ratio unit. Since this $1 \text{ unit} = 10 \text{ years}$, the scale is set. Now look at Subhash ($3$) and Prasad ($6$). They have a gap of exactly $3$ ratio units. Therefore, $3 \text{ units} \times 10 \text{ years} = 30 \text{ years}$. This takes under 5 seconds and requires zero algebra. ### Common Pitfall Many students waste valuable exam time unnecessarily calculating the exact individual ages of all three people ($30$, $60$, and $70$ years old) before performing the final subtraction, rather than just comparing the ratio units directly. ### Final Answer **Therefore, the correct answer is 30 years.**