In a particular shop, shirts are normally sold at 40% more than that of cost price during sale, shopkeeper normally gives 10% discount on selling price. If he solds 72 shirts of Rs 13,608 then cost price of each shirt is ?

Options

A. 210
B. 150
C. 149
D. 125

Answer

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

### Step 1: Calculate the Selling Price of One Shirt
We know that the total selling price (SP) for 72 shirts is Rs 13,608. To find the selling price of one shirt, we divide the total selling price by the number of shirts sold.

\[ \text{SP of one shirt} = \frac{13,608}{72} = 189 \]

### Step 2: Determine the Marked Price (MP)
The shopkeeper sells shirts at 40% more than the cost price (CP). Let's denote the cost price of one shirt as \( CP \). Therefore, the selling price (SP) can be expressed in terms of CP as:

\[ SP = CP + 0.4 \times CP = 1.4 \times CP \]

### Step 3: Account for the Discount
The shopkeeper gives a 10% discount on the selling price. Therefore, the actual selling price after the discount can be calculated as follows:

\[ \text{Discount} = 10\% \text{ of } SP = 0.1 \times SP \]
\[ \text{Actual SP} = SP - \text{Discount} = SP - 0.1 \times SP = 0.9 \times SP \]

Substituting the expression for SP from Step 2:

\[ \text{Actual SP} = 0.9 \times (1.4 \times CP) = 1.26 \times CP \]

### Step 4: Set Up the Equation
From Step 1, we know that the actual selling price of one shirt is Rs 189. Therefore, we can set up the equation:

\[ 1.26 \times CP = 189 \]

### Step 5: Solve for Cost Price (CP)
Now, we can solve for CP:

\[ CP = \frac{189}{1.26} \]
\[ CP = 150 \]

### Conclusion
The cost price of each shirt is Rs 150.

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