Question 67

If the gain is one-fifth of the selling price, then the gain percentage is:

Solution

Let the Cost Price = CP

Selling Price = SP

Given, gain is one-fifth of the selling price

$$=$$>  Gain = $$\frac{\text{SP}}{5}$$

$$=$$>  $$\text{SP}-\text{CP}=\frac{\text{SP}}{5}$$

$$=$$>  $$\text{CP}=\text{SP}-\frac{\text{SP}}{5}$$

$$=$$>  $$\text{CP}=\frac{4\text{SP}}{5}$$

$$\therefore\ $$Gain% = $$\frac{\text{Gain}}{\text{CP}}\times100$$

$$=\frac{\frac{\text{SP}}{5}}{\frac{4\text{SP}}{5}}\times100$$

$$=\frac{1}{4}\times100$$

$$=25\%$$

Hence, the correct answer is Option D


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