Discussion Forum

A, B and C enter into a partnership by investing in the ratio of 3 : 2: 4. After one year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs. 2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find the initial investment of each.

Answer:

Explanation:

Let the initial investments of $A$, $B$ and $C$ be Rs. $3x$, Rs. $2x$ and Rs. $4x$ respectively.

Then, $(3x\times 36)$ $:\left[(2x\times 12)+(2x+270000)\times 24\right]$ $:\left[(4x\times 24)+(4x+270000)\times 12\right]$

$=3:4:5$.

$\Rightarrow 108x$ $:(72x+6480000)$ $: (144x+3240000)$ $= 3:4:5$

$=\frac{108}{72x+6480000}$ $=\frac{3}{4}$ $=432x$ $=216x+19440000$

$\Rightarrow 216x$ $=19440000$ $\Rightarrow x=90000$.

Hence, A's initial investment $=3x$ = Rs. 2,70,000.

B's initial investment $=2x$ = Rs. 1,80,000.

C's initial investment $=4x$ = Rs. 3,60,000.