Two numbers are in the ratio 4 : 7. If 6 is added to each number, the ratio becomes 5 : 8. Find the larger number.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 42
Write the numbers as \(4x\) and \(7x\) and cross-multiply the new ratio.
\(\displaystyle \frac{4x+6}{7x+6}=\frac{5}{8}\)
\(32x+48=35x+30\)
\(3x=18\), so \(x=6\)
Numbers \(=24\) and \(42\)
Check: \(30:48=5:8\)
The larger number is 42.