Question

The selling price of $20$ articles is equal to the cost price of $22$ articles. Find the gain per cent.

Answer 1

Step 1: Find cost price and selling price.

Given: The selling price of $20$ articles is equal to the cost price of $22$ articles.

⇒ selling price of $20$ articles $=$ cost price of $22$ articles

⇒ $20\mathrm{S}.\mathrm{P}.=22\mathrm{C}.\mathrm{P}.$

⇒ $\frac{\mathrm{S}.\mathrm{P}.}{\mathrm{C}.\mathrm{P}.}=\frac{22}{20}$

⇒ $\frac{\mathrm{S}.\mathrm{P}.}{\mathrm{C}.\mathrm{P}.}=\frac{11}{10}$

Thus,

Cost price $=₨10$

Selling price $=₨11$

Step 2: Find the gain percent.

Since, $\mathrm{S}.\mathrm{P}.>\mathrm{C}.\mathrm{P}$, it will be a gain.

So, Gain = Selling price $-$ Cost price

Gain$=11-10=₨1$

Now,

Gain $\%$ $=\frac{\mathrm{Gain}}{\mathrm{C}.\mathrm{P}.}\times 100$

$$\begin{gathered} =\frac{1}{10}\times 100 \\ =\frac{100}{10} \\ =10\% \end{gathered}$$

Hence, the gain is $10\%$.