The present ages of Guru and Sonu are in the ratio 6 : 7 respectively. After 6 years their ages will be in the ratio 15 : 17 respectively. The present age of Guru is?
Understand the Problem
The question provides the current age ratio of Guru and Sonu and a future age ratio after 6 years, aiming to find Guru's present age among the provided options.
Answer
Guru's present age is $24$ years.
Answer for screen readers
Guru's present age is $24$ years.
Steps to Solve
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Define variables for ages Let Guru's current age be $6x$ and Sonu's current age be $7x$, according to the given ratio of their ages.
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Set up the future age equation After 6 years, Guru's age will be $6x + 6$ and Sonu's age will be $7x + 6$. The ratio of their ages at that time is given as 15:17. Thus, we can set up the equation: $$ \frac{6x + 6}{7x + 6} = \frac{15}{17} $$
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Cross-multiply to eliminate the fraction Cross-multiplying gives us: $$ 17(6x + 6) = 15(7x + 6) $$
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Expand both sides Expanding both sides results in: $$ 102x + 102 = 105x + 90 $$
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Rearrange to solve for x Now rearranging the equation gives: $$ 102x - 105x = 90 - 102 $$ Which simplifies to: $$ -3x = -12 $$ Thus: $$ x = 4 $$
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Calculate Guru's current age Substituting $x = 4$ into Guru's age: $$ \text{Guru's age} = 6x = 6(4) = 24 $$
Guru's present age is $24$ years.
More Information
At present, Guru is 24 years old, which fits both the current ratio and the future age ratio after 6 years. This is a typical problem involving ratios and can help in understanding age-related questions.
Tips
- Misinterpreting ratios: Ensure to set up the ratios accurately as given in the problem.
- Incorrect arithmetic: Double-check calculations when expanding and simplifying equations.
