A, B and C enter into a partnership by investing in the ratio of 3 : 2 : 4. After one year, B invests another ` 270000 and C, at the end of 2 years, also invests ` 270000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find the initial investment of each.
Answer
Answer (as printed):
Explanation
Let the initial investments of A, B and C be ₹$3x$, ₹$2x$ and ₹$4x$ respectively. Then, $(3x\times36):[(2x\times12)+(2x+270000)\times24]:[(4x\times24)+(4x+270000)\times12]=3:4:5$ $\Leftrightarrow 108x:(72x+6480000):(144x+3240000)=3:4:5$ $\therefore \frac{108x}{72x+6480000}=\frac{3}{4} \Leftrightarrow 432x=216x+19440000 \Leftrightarrow 216x=19440000 \Leftrightarrow x=90000$. Hence, A's initial investment $=3x=₹270000$; B's initial investment $=2x=₹180000$; C's initial investment $=4x=₹360000$.
Explanation as extracted from the printed page; notation may be imperfect.