Question : The ratio of two numbers is 3 : 5. If eight is added to the first, and seven to the second, then the ratio becomes 2 : 3. What will the ratio become if six is added to each?
Option 1: 9 : 14
Option 2: 5 : 7
Option 3: 5 : 9
Option 4: 7 : 9
Correct Answer: 9 : 14
Solution :
Take the two numbers as $3x$ and $5x$.
According to the given condition,
$\Rightarrow \frac{3x + 8}{5x + 7} = \frac{2}{3}$
$\Rightarrow 9x + 24 = 10x + 14$
$\Rightarrow x = 10$
So,
First number = $3\times 10 = 30$
Second number = $5\times 10 = 50$
Now, if 6 is added to each number, then the new ratio:
= (30 + 6) : (50 + 6)
= 36 : 56
= 9 : 14
Hence, the correct answer is 9 : 14.
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