A cloth merchant on selling 33 meters of cloth obtains a profit equal to the selling price of 11 meters of cloth the profit is = ?

Answer: Option C

Let the selling price of 1 meter cloth = Rs. 1
The Selling price of 33 meters cloth
= 1 × 33 = Rs. 33
Cost of 1 meter cloth = Rs. x
Cost price 33 meters cloth = x × 33 = Rs. 33x
According to the question,
Profit = Selling price - Cost price
$$\begin{array}{rl}& \Rightarrow 11=33-33x\\ & \Rightarrow 33x=22\\ & \Rightarrow x=\frac{22}{33}=\frac{2}{3}\end{array}$$
Cost price of 1 meter cloth $$=\text{Rs}\text{.}\frac{2}{3}$$
Cost price of 33 meters cloth
$$\begin{array}{rl}& =\frac{2}{3}\times 33\\ & =\text{Rs}.22\end{array}$$
Selling price of 33 meters cloth = Rs. 33
Profit = Selling price - Cost price
= 33 - 22 = 11
$$\begin{array}{rl}& \text{Profit}\%\\ & =\frac{11}{22}\times 100\\ & =50\%\end{array}$$