A, B and C enter into a partnership with capitals in the ratio $\frac{7}{2}: \frac{4}{3}: \frac{6}{5}$. After 4 months A increases his share of capital by 50%. If at the end of the year the total profit earned is ₹ 2430, find the share of each in the profit.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Ratio of capitals $=\frac{7}{2}: \frac{4}{3}: \frac{6}{5}=\left(\frac{7}{2} \times 30\right):\left(\frac{4}{3} \times 30\right):\left(\frac{6}{5} \times 30\right)=105: 40: 36$. Let the initial capitals of A, B and C be ₹ $105 x$, ₹ $40 x$ and ₹ $36 x$ respectively. Then, ratio of profits $=[105 x \times 4+(150 \%$ of $105 x) \times 8]:(40 x \times 12):(36 x \times 12)=1680: 480: 432=35: 10: 9$. $\therefore$ A's share $=₹\left(2430 \times \frac{35}{54}\right)=₹ 1575$; B's share $=₹\left(2430 \times \frac{10}{54}\right)=₹ 450$; C's share $=₹\left(2430 \times \frac{9}{54}\right)=₹ 405$.
Explanation as extracted from the printed page; notation may be imperfect.