Q. Two numbers are in the ratio 3:5, If 9 is subtracted from each, the new numbers are in the ratio 12:23. The smaller number is:

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Solution

The correct option is B 33
The numbers be 3x,5x
Then
$3 x - 9 = 12 y \to (1) 5 x - 9 = 23 y \to (2) (1) \times 5 - (2) \times 3 = - 45 + 27 = 60 y - 69 y = - 18 = - 9 y y = 2 x = \frac{33}{3} x = 11 Smallest number = 11 \times 3 = 33$

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