Two numbers are in the ratio 2 : 3. When 15 is added to both the numbers, the ratio becomes 11 : 14. Find the smaller number.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 18
Write the numbers as \(2x\) and \(3x\); adding 15 to each gives the new ratio, and equating it to 11 : 14 gives an equation in \(x\).
\(\displaystyle\frac{2x+15}{3x+15}=\frac{11}{14}\)
\(28x+210=33x+165\)
\(5x=45\), so \(x=9\)
Smaller number \(=2x=18\) (the numbers are 18 and 27)