Question

$A,B$ and $C$ started a business by investing Rs $800$, Rs $1600$ and Rs$2000$ respectively. After a quarter they invested amounts in a ratio $1:4:2$. After another quarter, they invested amounts in ratio $3:2:3$.In the last quarter the ratio of investments was same as in $2^{nd}$ quarter. Also in the last quarter, the respective amounts of $A,B$ and $C$ was double than the respective amounts invested in $2^{nd}$ quarter. The total investment of $C$ before $4^{th}$ quarter was Rs $1400$ more than that of $A$ during same duration. Also ratio of $B^{\prime }s$ share in profit to total profit at the end of year was $66:153$.

If $B^{\prime }s$ investment for both the terms ($4$ months and $8$ months) was swapped, then find the total profit share of $B$ and $C$ if annual profit is Rs $46,200$.

Answer 1

Quarters means $3$ months each

Ratio of investments in $2^{nd}$ quarter – $1:4:2$, so let amounts – $x,4x,2x$

Ratio of investments in 3rd quarter – $3:2:3$, so let amounts – $3y,2y,3y$

In last quarter, respective amount is double then in $2^{nd}$ quarter, so amounts – $2x,8x,4x$

In the last quarter the ratio of investments was same as in $2^{nd}$ quarter. — this is not required to solve question.

Given:

$(2000+2x+3y)=1400+(800+x+3y)$

$\Rightarrow 2000+2x+3y-1400-800-x-3y=0$

$\Rightarrow x-200=0$

or $x=$ Rs $200$

Now ratio of profit share —$A:B:C$ is

$800\times 3+x\times 3+3y\times 3+2x\times 3:1600\times 3+4x\times 3+2y\times 3+8x\times 3:2000\times 3+2x\times 3+3y\times 3+4x\times 3$

$3$ gets cancelled, gives

$(800+3x+3y):(1600+12x+2y):(2000+6x+3y)$

Put $x=200$ gives

$1400+3y:4000+2y:3200+3y$

Now given

$\frac{(4000+2y)}{(1400+3y+4000+2y+3200+3y)}=\frac{66}{153}$

$\frac{(2000+y)}{(4300+4y)}=\frac{22}{51}$

Solve,$y=Rs200$

So now the total investment is—$(800+3x+3y)+(1600+12x+2y)+(2000+6x+3y)=(4400+21x+8y)$

put $x=200,y=200$, total investment $=$ Rs $10,200$