The ratio of the profits of P and Q is 7 : 5, and that of Q and R is 15 : 10. If P, Q and R kept their money in the business for 1 year, 2 years and 5 years respectively, find the ratio P : Q : R of their investments.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 42 : 15 : 4
Profit \(\propto\) capital \(\times\) time, so capital \(\propto\) profit \(\div\) time. First the two profit ratios are joined into one, then each part is divided by its time.
Q : R \(=15:10=3:2\)
Making Q the same in both: P : Q \(=7:5=21:15\) and Q : R \(=3:2=15:10\)
P : Q : R (profits) \(=21:15:10\)
Capitals \(\displaystyle =\frac{21}{1}:\frac{15}{2}:\frac{10}{5}=21:7.5:2\)
Multiplying by 2: \(42:15:4\)
The investments are in the ratio 42 : 15 : 4.