Question

three friends started a business with ₹19500, ₹27300, ₹15600 respectively. after one year profit was ₹43200. if they divided ⅔ of this profit equally among themselves and the remaining in the ratio of their capitals, find the share of each of them.
(plz answer step-by-step)​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{The capitals the three people} =\text{Rs. } 19500; \text{Rs. }27300;\text{Rs. }15600$

       $\text{Total profit amount}= \text{Rs. }43200$

       $\text{The question states that, }\frac{2}{3} \text{ of the profit was equally distributed}$

$\implies \dfrac{2}{3} \times 43200 = 2\times 14400 = \text{Rs. }28800 \text{ was distributed equally}$

$\implies \text{Each person got}= \dfrac{28800}{1+1+1} = \dfrac{28800}{3} = \text{Rs. }9600$

       $\text{The question also states that the remaining profit was distributed in} \\\text{the ratio of their capitals}$

$\implies \text{The remaining profit} = 43200 - 28800 = \text{Rs. }14400$

       $\text{The ratio of their capitals} = 19500:27300:15600$

                                                 $\text{Dividing by 100}$

                                                 $\text{ }= 195:273:156$

                                                 $\text{Dividing by 39}$

                                                 $\text{ }= 5:7:4$

$\implies \text{Share of remaining profits for:}$

       $1^{st} \text{ person} = \dfrac{5}{5 + 7 +4}\times 14400 = \dfrac{5}{16}\times 14400 = \text{Rs. }4500$

       $2^{nd} \text{ person} = \dfrac{7}{5 + 7 +4}\times 14400 = \dfrac{7}{16}\times 14400 = \text{Rs. }6300$

       $3^{rd} \text{ person} = \dfrac{4}{5 + 7 +4}\times 14400 = \dfrac{4}{16}\times 14400 = \text{Rs. }3600$

$\implies \text{Share of total profit received by: }$

       $\boxed{1^{st} \text{ person} = 4500 + 9600 = \text{Rs. }14100}$

       $\boxed{2^{nd} \text{ person} = 6300 + 9600 = \text{Rs. }15900}$

       $\boxed{3^{rd} \text{ person} = 3600 + 9600 = \text{Rs. }13200}$