Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each, the ratio becomes 12 : 23. Find the greater number.

55

The correct answer is Option (1) → 55

Step 1: Let the numbers be

$3x \text{ and } 5x$

Step 2: Condition after subtracting 9

$\frac{3x - 9}{5x - 9} = \frac{12}{23}$

Step 3: Cross-multiply

$23(3x - 9) = 12(5x - 9)$

$69x - 207 = 60x – 108$

$69x - 60x = -108 + 207$

$9x=99$

$x = 11$

Step 4: Find the numbers

$3x = 3 \cdot 11 = 33 \quad (\text{smaller})$

$5x = 5 \cdot 11 = 55 \quad (\text{greater})$