A trader had 22 quintals of wheat. He sold a part of it at 23% profit and the rest at 33% profit, so that he made a total profit of 27%. How much wheat did he sell at 33% profit?

Let the C.P. of 1 quintal of wheat be Re.1. Let the quantity of wheat sold at 33% profit be x quintals. ∴ Quantity of wheat sold at 23% profit = (22 – x) quintals According to the question, $x \times \frac{33}{100}+(22-x) \times \frac{23}{100}$ $=22 \times \frac{27}{100}$ $\Rightarrow 33 x+22 \times 23-23 x=22 \times 27$ $\Rightarrow 10 x+506=594$ $\Rightarrow 10 x=594-506=88$ $\Rightarrow x=\frac{88}{10}=8.8$ quintals $=(8.8 \times 100) \mathrm{kg} .=880 \mathrm{~kg} .$ Alternative:

According to the question,

5 unit $\rightarrow 22$

2 unit $\rightarrow \frac{22}{5} \times 2$

$=8.8$ quintals

$=8.8 \times 100=880 \mathrm{~kg}$