If the ratio between the profit and selling price of an article is 1:5, then the ratio between the selling price and the cost price of that article is:

Options

A. `3:2`
B. `4:3`
C. `5:4`
D. `6:5`

Answer

To solve the problem, we need to find the ratio between the selling price (SP) and the cost price (CP) of an article given that the ratio between the profit and selling price is 1:5.

**Step-by-step solution:**

1. **Understand the given ratio**:
We are given that the ratio of profit (P) to selling price (SP) is 1:5. This can be expressed mathematically as:
\[ \frac{P}{SP} = \frac{1}{5} \]

2. **Express profit and selling price in terms of a variable**:
Let the profit be \( P = 1x \) and the selling price be \( SP = 5x \), where \( x \) is a common multiplier.

3. **Calculate the cost price (CP)**:
The cost price can be calculated using the formula:
\[ CP = SP - P \]
Substituting the values we have:
\[ CP = 5x - 1x = 4x \]

4. **Find the ratio of selling price to cost price**:
Now, we need to find the ratio of selling price (SP) to cost price (CP):
\[ \frac{SP}{CP} = \frac{5x}{4x} \]
Simplifying this gives:
\[ \frac{SP}{CP} = \frac{5}{4} \]

5. **Conclusion**:
The ratio between the selling price and the cost price of the article is \( 5:4 \).

**Final Answer**: The ratio between the selling price and the cost price is \( 5:4 \) (Option C).

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