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.

Explanation:-

Let the quantity sold at 18% profit be 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] $$\eqalign{ & = {\text{Rs}}.\left[ {\frac{{27}}{{25}}\left( {100 - x} \right) + \frac{{59x}}{{50}}} \right] = {\text{Rs}}.\left( {1080 + \frac{x}{{10}}} \right). \cr & \therefore 1080 + \frac{x}{{10}} = 114\% {\text{ of }}1000 \cr & \Rightarrow 1080 + \frac{x}{{10}} = 1140. \cr & \Rightarrow \frac{x}{{10}} = 60 \cr & \Rightarrow x = 600. \cr}$$