The ratio of cost price to the selling price of an article is 5 : 6. If 20% discount is offered on marked price of the article then marked price is what percent more than cost price?

Options

A. `(100)/(3)%`
B. 0.5
C. 0.4
D. `(200)/(3)%`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Define the Cost Price and Selling Price
Given the ratio of Cost Price (CP) to Selling Price (SP) is 5:6, we can express them in terms of a variable \( y \):
- Cost Price (CP) = \( 5y \)
- Selling Price (SP) = \( 6y \)

**Hint:** Use a variable to represent the common factor in the ratio.

### Step 2: Calculate the Marked Price
Let the Marked Price (MP) be \( x \). Since a 20% discount is offered on the marked price, the selling price can be expressed as:
\[ SP = MP - (20\% \text{ of } MP) = MP \times (1 - 0.20) = MP \times 0.80 \]
Thus, we can write:
\[ 6y = 0.80x \]

**Hint:** Remember that a discount reduces the price by a certain percentage of the marked price.

### Step 3: Solve for the Marked Price
From the equation \( 6y = 0.80x \), we can solve for \( x \):
\[ x = \frac{6y}{0.80} = \frac{6y}{\frac{4}{5}} = 6y \times \frac{5}{4} = \frac{30y}{4} = 7.5y \]

**Hint:** When dividing by a fraction, multiply by its reciprocal.

### Step 4: Calculate the Percentage Increase of Marked Price over Cost Price
Now we have:
- Cost Price (CP) = \( 5y \)
- Marked Price (MP) = \( 7.5y \)

To find out what percent more the marked price is than the cost price, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{MP - CP}{CP} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{7.5y - 5y}{5y} \right) \times 100 = \left( \frac{2.5y}{5y} \right) \times 100 = \left( \frac{2.5}{5} \right) \times 100 = 50\% \]

**Hint:** The percentage increase is calculated by taking the difference between the two values, dividing by the original value, and then multiplying by 100.

### Final Answer
The marked price is **50% more** than the cost price.

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