The difference between two numbers P and Q (P > Q) is 40% of their sum. The ratio P : Q is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 7 : 3
40% is \(\frac{2}{5}\), so the question says \(P-Q=\frac{2}{5}(P+Q)\).
\(5(P-Q)=2(P+Q)\)
\(5P-5Q=2P+2Q\)
\(3P=7Q\)
\(P:Q=7:3\)
Shortcut: By componendo and dividendo, a ratio of difference to sum can be turned straight into the ratio of the two numbers:
\(\displaystyle\frac{P-Q}{P+Q}=\frac{2}{5}\) gives \(\displaystyle\frac{P}{Q}=\frac{5+2}{5-2}=\frac{7}{3}\)