Raghu sold an article for ₹180 after allowing a 20% discounton its marked price. Had he not allowed any discount, he would have gained 20%. What is the cost price of the article?

Options

A. ₹190.40
B. ₹192.80
C. ₹188.60
D. ₹187.50

Answer

To find the cost price of the article sold by Raghu, we can follow these steps:

### Step 1: Determine the Marked Price
Let the marked price of the article be \( M \).

Given that Raghu sold the article for ₹180 after allowing a 20% discount, we can express this as:
\[ \text{Selling Price (SP)} = M - 0.2M = 0.8M \]
Thus, we have:
\[ 0.8M = 180 \]

### Step 2: Solve for Marked Price
To find \( M \), we can rearrange the equation:
\[ M = \frac{180}{0.8} = 225 \]

### Step 3: Determine Selling Price without Discount
If no discount was allowed, the selling price would be equal to the marked price:
\[ \text{Selling Price without discount} = M = 225 \]

### Step 4: Calculate Cost Price
We know that if Raghu had sold the article at the marked price (₹225), he would have gained a profit of 20%. Let the cost price be \( C \).

The selling price with a 20% profit can be expressed as:
\[ \text{Selling Price} = C + 0.2C = 1.2C \]
Setting this equal to the selling price without discount, we have:
\[ 1.2C = 225 \]

### Step 5: Solve for Cost Price
Now, we can solve for \( C \):
\[ C = \frac{225}{1.2} = 187.5 \]

Thus, the cost price of the article is ₹187.50.

### Final Answer
The cost price of the article is **₹187.50**.

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