Discussion

Explanation:

Hint: Students please note that the percentages that are given are the basic percentages derived from basic fractions. e.g. 11.11% = $\frac{1}{9}$ and 14.28 = $\frac{1}{7}.$

Hence, you should make use of the most of this kind of knowledge. So let the CP be Re 1. Since he makes a profit of $\frac{1}{7},$ his SP = $\left(1+\frac{1}{7}\right)=\mathrm{Rs}. \frac{8}{7}$.

His marked price should be $\frac{1}{9}$ above this. So if we subtract $\frac{1}{9}$ of MP from the MP, we will get the SP.
So $\left(\mathrm{MP}-\frac{1}{9}\mathrm{MP}\right)=\mathrm{SP}=\frac{8}{7}$

Hence, MP = $\frac{9}{7}$

Therefore, percentage of mark-up on CP = (MP – CP)/CP

$=\left(\frac{9}{7}-1\right)/1=\frac{2}{7}=2\left(\frac{1}{7}\right)$ = 2 × 14.28 = 28.56%

Alternative method:
We can use the formula z = x – y – $\frac{xy}{100},$ where
z = Gain percentage
x = Percentage above CP
y = Discount percentage
∴ 14.28% = x – 11.11% – $\frac{11.11x}{100}$

or 14.28 = $\frac{100x-1111-11.11x}{100}$

or 1428 - 1111 = 88.89x

or x = 28.56% (Approximately)

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