A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity (in kg) sold at 18% profit is.

Answer: Option C

Let the quantity sold at 18% profit be $$x$$ kg and let C.P. per kg be Rs. 1
Then,
quantity sold at 8% profit = (1000 - $$x$$) kg.
Total C.P. = Rs. 1000
Total S.P. = Rs. [108% of (1000 - x) + 118% of $$x$$]
  $$=\text{Rs}.\left[\frac{27}{25}\left(1000-x\right)+\frac{59x}{50}\right]$$      $$=\text{Rs}.\left(1080+\frac{x}{10}\right)$$
$$\begin{array}{rl}& \therefore 1080+\frac{x}{10}=114\%\text{ of }1000\\ & \Rightarrow 1080+\frac{x}{10}=1140.\\ & \Rightarrow \frac{x}{10}=60\\ & \Rightarrow x=600\end{array}$$