Arithmetic: Partnership Test -2

Ratio of profit
$\displaystyle \begin{array}{l}=x\times 12:2x\times 6:3x\times 4\\=1:1:1\\\therefore \,\,\,C's\,\,\,share=\frac{1}{3}\times 27000\\=Rs.\,9000\end{array}$

Gaining ratio
$\displaystyle \begin{array}{l}=\left( \frac{3}{5}-\frac{4}{9} \right):\left( \frac{2}{5}-\frac{2}{9} \right)\\=\frac{27-20}{45}:\frac{18-10}{45}=7:8\end{array}$

Ratio of the Profit = Ratio of the equivalent capitals of Karan and Shirish for 1 month
$\displaystyle \begin{array}{l}=60000\times 12:100000\times 6\\=720000:600000=6:5\\\therefore \,\,\,Shirish's\,\,\,share\,\,\,in\,\,the\,\,\,profit\\=Rs.\,\left( \frac{5}{11}\times 151800 \right)=Rs.69000\end{array}$

Ratio of the equivalent capitals of Prakash, Sunil and Anil for 1 month
= 11 X 36: 16.5 X 36 : 8.25 X 36
= 4:6:3
Therefore Anil’s share in the profit
{3/(4+6+3)} X 19.5
= 4.5 lakh
Therefore 50% of 4.5
2.25 lakh

Let Mona’s investment=Rs.100
Therefore Sonu’s investment = Rs.110
And Raghu’s investment
$\displaystyle =Rs.\,\frac{1000}{9}$
Therefore Ratio of Mona’s, Sonu’s and Raghu’s investments
$\displaystyle =100:110:\frac{1000}{9}=90:99:100$
Sum of ratios = 90 + 99 + 100 = 289
Therefore Raghu’s investment
$\displaystyle =Rs.\,\left( \frac{100}{289}\times 5780 \right)=Rs.2000$