The present ages of the two people are 46 years and 60 years, respectively. If after 'k' years, the ratio of t

Question

The present ages of the two people are 46 years and 60 years, respectively. If after 'k' years, the ratio of their ages is 4:5, then the value of 'k' is:

Examoogle · Accepted Answer

The correct answer is Option B: 10. Use the cross-multiplication method: $5(46+k) = 4(60+k) \Rightarrow 230 + 5k = 240 + 4k$. Subtract $4k$ and $230$ from both sides to get $k = 10$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the cross-multiplication method: $5(46+k) = 4(60+k) \Rightarrow 230 + 5k = 240 + 4k$. Subtract $4k$ and $230$ from both sides to get $k = 10$.

Formula Used: $$\frac{46 + k}{60 + k} = \frac{4}{5}$$

Given: Present ages of two people are 46 and 60 years. Ratio after k years is 4:5.

Steps: Define the relationship: Let the present ages be $46$ and $60$. After $k$ years, the ages become $(46+k)$ and $(60+k)$. The problem states their ratio is $4:5$.. Solve for k: Cross-multiply the equation to solve for $k$: $5 	imes (46 + k) = 4 	imes (60 + k)$.. Isolate the variable: Subtract $4k$ from both sides and $230$ from both sides to find $k$.

Answer: B is correct because the cross-multiplication of the age ratio equation $$\frac{46+k}{60+k} = \frac{4}{5}$$ results in $k = 10$.

Exam Tip: This ratio-based algebraic approach is identical to mixture and allegation problems where you find an amount to be added to balance a ratio.

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