A dealer allows 30% discount on the marked price of an item and still makes a profit of 10%. By how much percentage is the marked price more than the cost price (rounded off to two places of decimal)?

Correct option is A

Given:
Discount on marked price = 30%
Profit = 10% 

Formula Used: 

Selling Price (SP) = MP - Discount 

SP = CP + Profit 

the percentage difference between MP and CP:

​$$=\frac{\text{MP} - \text{CP}}{\text{CP}} \cdot 100$$

Solution:

Discount = $$30\% \, \text{of MP} = 0.3 \cdot \text{MP}$$​​

Profit = $$10\% \text{ of CP} = 0.1 \cdot \text{CP}$$

​​Selling Price (SP) = MP - 0.3MP = 0.7MP

So,

​$$0.7 \, MP = CP + 0.1 \, CP \\ \ \\0.7 \, MP = 1.1 \, CP \\ \ \\ MP = \frac{1.1 CP}{0.7}$$​​

Now, the percentage difference between MP and CP:

​$$= \frac{\left(\frac{1.1 \cdot \text{CP}}{0.7}\right) - \text{CP}}{\text{CP}} \cdot 100$$​​

​$$= \left( \frac{1.1}{0.7} - 1 \right) \cdot 100 \approx \bf 57.14\%$$  

Alternate Method: 

$$\frac{MP}{CP} = \frac{100 + \text{profit} \%}{100 - \text{discount} \%} \\ \ \\ \frac{MP}{CP} = \frac{100+10}{100 - 30} \\ \ \\ \frac{MP}{CP} = \frac{110}{70} \\ \ \\ \frac{MP}{CP} = \frac{11}{7}$$  

Now,  Percentage difference = $$\frac{4}{7}\times 100 \approx \bf 57.14 \%$$​​