The profit by selling an item was 25%. If the item was marked 40% above the selling price then what is the ratio of the marked price to the cost price of the item?

Options

A. `5/4`
B. `7/4`
C. `3/5`
D. `1/4`

Answer

To solve the problem, we need to find the ratio of the marked price (MP) to the cost price (CP) of the item given the profit percentage and the relationship between the marked price and the selling price.

### Step 1: Define the variables
Let:
- Cost Price (CP) = \( x \)
- Selling Price (SP) = \( y \)
- Marked Price (MP) = \( z \)

### Step 2: Use the profit percentage
We know that the profit is 25%. This means:
\[ SP = CP + \text{Profit} \]
Given that profit is 25% of CP:
\[ SP = CP + 0.25 \times CP = 1.25 \times CP \]
Thus, we can write:
\[ y = 1.25x \]

### Step 3: Use the relationship between marked price and selling price
The problem states that the item was marked 40% above the selling price. This means:
\[ MP = SP + 0.40 \times SP = 1.40 \times SP \]
Substituting the expression for SP from Step 2:
\[ z = 1.40 \times y = 1.40 \times (1.25x) \]
Calculating this gives:
\[ z = 1.40 \times 1.25x = 1.75x \]

### Step 4: Find the ratio of marked price to cost price
Now we have:
- Marked Price (MP) = \( 1.75x \)
- Cost Price (CP) = \( x \)

The ratio of the marked price to the cost price is:
\[ \frac{MP}{CP} = \frac{1.75x}{x} = 1.75 \]
This can also be expressed as a fraction:
\[ \frac{MP}{CP} = \frac{1.75}{1} = \frac{7}{4} \]

### Final Answer
The ratio of the marked price to the cost price of the item is \( \frac{7}{4} \).

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