Question : Two numbers are in the ratio 3 : 5. If 6 is added to each of them the ratio becomes 2 : 3. The numbers are:
Option 1: 21 and 35
Option 2: 30 and 50
Option 3: 24 and 40
Option 4: 18 and 30
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Correct Answer: 18 and 30
Solution :
Let the numbers be $3x$ and $6x$.
According to the question,
$\frac{3x+6}{5x+6}$ = $\frac{2}{3}$
$⇒ 9x+ 18 = 10x + 12$
$\therefore x= 6$
Therefore, the numbers are (3 × 6) = 18 and (5 × 6) = 30
Hence, the correct answer is 18 and 30.
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