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
Numbers in the ratio 3 : 5 can be written as \(3x\) and \(5x\); subtracting 9 from each gives a new ratio, which fixes \(x\).
After 9 is subtracted, the ratio is 12 : 23: \(\displaystyle \frac{3x-9}{5x-9}=\frac{12}{23}\)
\(23(3x-9)=12(5x-9)\), that is, \(69x-207=60x-108\)
\(69x-60x=207-108\), so \(9x=99\) and \(x=11\)
The numbers are \(3\times11=33\) and \(5\times11=55\), so the greater number is 55