By selling 33 metres of cloth a person gains the cost price of 11 metres find his gain

Solution(By Examveda Team)

Let Selling price of 1 meters cloth = Rs. 1
Selling price of 33 meters cloth = Rs. 33
Cost price of 1 meter cloth = Rs. x
Cost price of 33 meters cloth = Rs. 33x
According to the question,
Profit = Selling price - Cost price
$$\eqalign{ & \Rightarrow 11x = 33 - 33x \cr & \Rightarrow 44x = 33 \cr & \Rightarrow x = \frac{{33}}{{44}} = \frac{3}{4} \cr & {\text{Cost price of 1 metre}} \cr & = {\text{Rs}}{\text{.}}\frac{3}{4} \cr & {\text{Cost price of 33 metres}} \cr & = \frac{3}{4} \times 33 \cr & = {\text{Rs}}.\frac{{99}}{4} \cr} $$
Selling price of 33 meters = Rs. 33
Profit = Selling price = Cost price
$$\eqalign{ & = 33 - \frac{{99}}{4} \cr & = \frac{{33}}{4} \cr & \therefore {\text{Profit }}\% \cr & {\text{ = }}\frac{{\frac{{33}}{4}}}{{\frac{{99}}{4}}} \times 100 \cr & = \frac{{33}}{{99}} \times 100 \cr & = \frac{1}{3} \times 100 \cr & = 33\frac{1}{3}\% \cr} $$

Alternate :
Let Selling price of 1 meters cloth = Rs. 1
Selling price of 33 meters cloth = Rs. 33
33 Selling price - 33 Cost price = 11 Cost price
33 Selling price = 44 Cost price
$$\eqalign{ & \frac{{{\text{Selling price}}}}{{{\text{Cost price}}}} = \left. {\frac{4}{3}} \right\rangle 1 \cr & {\text{Profit = 1}} \cr & {\text{Profit }}\% = \frac{1}{3} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 33\frac{1}{3}\% \cr} $$