A shopkeeper marks the price of the article in such a way that after allowing 28% discount, he wants a gain of 12%. If the marked price is Rs. 224, then the cost price of the article is :

Options

A. Rs. 144
B. Rs. 168
C. Rs. 196
D. Rs. 120

Answer

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

### Step 1: Identify the given values
- Marked Price (MP) = Rs. 224
- Discount = 28%
- Desired Profit = 12%

### Step 2: Calculate the Selling Price (SP)
The Selling Price after discount can be calculated using the formula:
\[ SP = MP \times \left(1 - \frac{Discount}{100}\right) \]
Substituting the values:
\[ SP = 224 \times \left(1 - \frac{28}{100}\right) \]
\[ SP = 224 \times \left(1 - 0.28\right) \]
\[ SP = 224 \times 0.72 \]
\[ SP = 161.28 \]

### Step 3: Calculate the Cost Price (CP)
To find the Cost Price, we can use the formula:
\[ CP = \frac{100}{100 + Profit\%} \times SP \]
Substituting the values:
\[ CP = \frac{100}{100 + 12} \times 161.28 \]
\[ CP = \frac{100}{112} \times 161.28 \]

### Step 4: Simplify the calculation
Now, we can simplify:
\[ CP = \frac{100 \times 161.28}{112} \]
Calculating the numerator:
\[ 100 \times 161.28 = 16128 \]
Now divide by 112:
\[ CP = \frac{16128}{112} \]
Calculating this gives:
\[ CP = 144 \]

### Final Answer
Thus, the cost price of the article is Rs. 144.

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