A, B and C started a business. A invested 30% of the total capital, B invested \(14\frac{2}{7}\%\) of the remaining capital and C invested the rest. If their money stayed in the business for 2 years, 1 year and 6 months respectively, find the ratio A : B : C of their profits at the end.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6 : 1 : 3
Profit is shared in the ratio of capital × time. First the shares of the capital are found as percentages of the whole, then each is multiplied by its time in months.
A’s capital \(=30\%\), so the remaining capital \(=70\%\)
\(14\frac{2}{7}\%=\frac{1}{7}\), so B’s capital \(\displaystyle =\frac{1}{7}\times70\%=10\%\)
C’s capital \(=70\%-10\%=60\%\)
Times: 2 years \(=24\) months, 1 year \(=12\) months, 6 months
A : B : C \(=30\times24:10\times12:60\times6=720:120:360\)
Dividing by 120: \(6:1:3\)
The profits are in the ratio 6 : 1 : 3.