Two numbers are in the ratio of 3 : 5. If 9 is subtracted from each, the ratio becomes 12 : 23. Find the greater number.
Answer & explanation
Correct answer: option 1
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
$3x = 3 \cdot 11 = 33 \quad (\text{smaller})$
$5x = 5 \cdot 11 = 55 \quad (\text{greater})$