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.

Solution(By Examveda Team)

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