At present, Suresh's age is twice the age of his daughter. After 6 years from now, the ratio of the ages of Suresh and his daughter will be $23 : 13$. What is the present age of Suresh?

### Concept & Formula The logic revolves around defining present ages using a multiplier (twice), advancing those ages into the future mathematically, and equating them to a newly given ratio. ### Step-by-Step Solution * **Given:** * Present: Suresh = $2 \times$ Daughter * Future ($+6$ years): Suresh : Daughter = $23 : 13$ * **Calculation / Deduction:** * Let the daughter's present age be $x$. * Then, Suresh's present age is $2x$. * After $6$ years, their ages will be: * Daughter = $x + 6$ * Suresh = $2x + 6$ * The problem states the future ratio is $23 : 13$. Set up the equation: * $$\frac{2x + 6}{x + 6} = \frac{23}{13}$$ * Cross-multiply to solve for $x$: * $$13(2x + 6) = 23(x + 6)$$ * $$26x + 78 = 23x + 138$$ * Group the variables and constants: * $$26x - 23x = 138 - 78$$ * $$3x = 60$$ * $$x = 20$$ * The daughter's present age is $20$. * Suresh's present age = $2x = 2 \times 20 = 40$ years. ### Exam Strategy & Shortcut Use Option Elimination with Divisibility Rules. Suresh's present age must be an even number (since he is twice his daughter's age). All given options are even. After $6$ years, Suresh's age must be a multiple of $23$ (from the $23:13$ ratio). Let's test the options by adding $6$: (a) $36 + 6 = 42$ (Not divisible by 23) (b) $40 + 6 = 46$ (Divisible by 23, since $23 \times 2 = 46$) (c) $46 + 6 = 52$ (Not divisible by 23) Option (b) is the only mathematically viable answer. This takes 10 seconds and requires zero algebra. ### Common Pitfall Students often incorrectly place the $6$ years. They might multiply the present ratio by $6$ or forget to add $6$ to *both* the numerator and denominator when setting up the future fraction. Always remember that time passes equally for both individuals. ### Final Answer **Therefore, the correct answer is 40 years.**