The sum of the ages of Jayant, Prem and Paras is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Paras?

### Concept & Logic To use a past ratio, you must adjust the present sum to match the past timeframe. Subtract the elapsed time for *each* person involved before distributing the total according to the ratio. $$ \text{Past Sum} = \text{Present Sum} - (n \times \text{years}) $$ ### Step-by-Step Solution * **Given:** Present sum = 93. Ratio 10 years ago = $2:3:4$. Number of people = 3. * **Calculation:** Find the sum of their ages 10 years ago. * Past sum = $93 - (3 \times 10) = 93 - 30 = 63$ years. * 10 years ago, their ages were $2x, 3x$, and $4x$. * Equation: $2x + 3x + 4x = 63 \implies 9x = 63 \implies x = 7$. * Paras's ratio share 10 years ago was $4x$. * Paras's age 10 years ago = $4 \times 7 = 28$ years. * Paras's present age = $28 + 10 = 38$ years. ### Exam Strategy & Shortcut **Option Alignment:** The question asks for the present age of Paras. Since his ratio 10 years ago was 4, his (Present Age - 10) must be a multiple of 4. Check the options: (a) $24 - 10 = 14$ (No) (b) $28 - 10 = 18$ (No) (c) $32 - 10 = 22$ (No) (d) $34 - 10 = 24$ (Yes) (e) $38 - 10 = 28$ (Yes) We have two candidates. But 34 implies $x=6$, making past sum 54, which doesn't match 63. So 38 is the only correct answer. ### Common Pitfall Finding the age 10 years ago (28) and forgetting to add 10 to get the *present* age. Examiners frequently put 28 in the options as a trap (Option B). ### Final Answer Therefore, the correct answer is **38 years**.