Question

$P,Q$ and $R$ start a business with Rs $30,000,$ Rs $40,000$ Rs $50,000$ respectively. $P$ stays for the entire year. $Q$ leaves the business after two months but rejoins after another $4$ months but only $\frac{3}{4}$ of his initial capital. $R$ leaves after $3$ months and rejoins after another $5$ months but with only $\frac{4}{5}$ of his capital. If the year end profit is Rs $27,900$, how much more than $Q$ did $R$ get?

Answer 1

$P^{\prime }$s total investment $=30000\times 12=360000$ Rs

$Q^{\prime }$s total investment $=40000\times 2+\frac{3}{4}\times 40000\times 6=80000+180000=260000$ Rs

$R^{\prime }$s total investment $=50000\times 3+\frac{4}{5}\times 50000\times 4=150000+160000=310000$ Rs

Ratio of their investment:

$\Rightarrow 360000:260000:310000$

$\Rightarrow 36:26:31$

Total profit is Rs $27900$

Let the common profit ratio be $x$ Rs.

Then,

$(36+26+31)\times x=27900$

$93x=27900$

$x=300$ Rs.

Difference between $Q^{\prime }$s and $R^{\prime }$s profit,

$\Rightarrow (31-26)\times x$

$\Rightarrow 5\times 300$

$\Rightarrow 1500$ Rs.

Thus Difference between $Q^{\prime }$s and $R^{\prime }$s profit $=1500$ Rs.