P, Q, R formed a company in partnership. P invested one-third of the capital while Q invested half of the capital.
Rest was invested by R. If the company earned Rs.1200 at the end of one year, what was the profit share of R?

P's investment = 1/3 of total capital

​Q's investment = 1/2 of total capital

R's investment = 1 - (1/3 + 1/2) = 1/6 of total capital

Total profit = Rs. 1200

Ratio and Proportion

​Ratio of P's, Q's, and R's investments = $$\frac{1}{3} : \frac{1}{2} : \frac{1}{6} = 2 : 3 : 1$$​​

Total parts = 2 + 3 + 1 = 6

​$$R's\ \text{share of profit} = \left(\frac{\text{R's investment}}{\text{Total investment}}\right) \times \text{Total profit} \\[10pt]= \left(\frac{1}{6}\right) \times 1200 \\[10pt]= \text{Rs. } 200$$​​