Two friends P and Q started a business investing in the ratio 5 : 6. R joined them after six months investing an amount equal to that of Q's. At the end of the year, 20% profit was earned which was equal to Rs. 98000. What was the amount invested by R?

Let the total investment be Rs. z
Then,
$$\eqalign{ & 20\% {\text{ of }}z = 98000 \cr & \Leftrightarrow z = \left( {\frac{{98000 \times 100}}{{20}}} \right) \cr & \Leftrightarrow z = 490000 \cr} $$
Let the capital of P, Q and R be
Rs. 5x, Rs. 6x and Rs. 6x respectively
Then,
$$ \Leftrightarrow \left( {5x \times 12} \right)$$   + $$\left( {6x \times 12} \right)$$   + $$\left( {6x \times 6} \right)$$ &nbsp = $$490000 \times 12$$
$$\eqalign{ & \Leftrightarrow 168x = 490000 \times 12 \cr & \Leftrightarrow x = \left( {\frac{{490000 \times 12}}{{168}}} \right) \cr & \Leftrightarrow x = 35000 \cr & \therefore {\text{R's investment}} \cr & = {\text{Rs}}{\text{. }}6x \cr & = {\text{Rs}}{\text{.}}\left( {6 \times 35000} \right) \cr & = {\text{Rs}}{\text{. 210000}} \cr} $$