MP of a chair is 37.5% more than its CP. If SP and MP both are increased by `44 (4)/(9)%`, then profit becomes 3 times. If the initial MP of chair is Rs.3850, then find initial SP of chair.

Options

A. Rs. 3600
B. Rs. 4500
C. Rs. 3150
D. Rs. 4050

Answer

To solve the problem step by step, we will follow the information given in the question and apply mathematical operations accordingly.

### Step 1: Understand the relationship between CP and MP
The mark price (MP) of the chair is given to be 37.5% more than its cost price (CP). We can express this relationship mathematically as:
\[ MP = CP + 0.375 \times CP = 1.375 \times CP \]
Given that the initial MP is Rs. 3850, we can set up the equation:
\[ 3850 = 1.375 \times CP \]

### Step 2: Calculate the Cost Price (CP)
To find the cost price (CP), we rearrange the equation:
\[ CP = \frac{3850}{1.375} \]
Now, we will perform the division:
\[ CP = \frac{3850 \times 1000}{1375} = \frac{3850000}{1375} \]
Now, simplifying \( \frac{3850000}{1375} \):
\[ CP = 2800 \text{ Rs.} \]

### Step 3: Set up the equation for Selling Price (SP)
Let the initial selling price (SP) be \( x \). The profit can be calculated as:
\[ \text{Profit} = SP - CP = x - 2800 \]

### Step 4: Calculate the new Selling Price (SP) after the increase
Both the SP and MP are increased by \( \frac{44}{9}\% \). To calculate the new SP:
\[ \text{New SP} = x + \frac{44}{9}\% \text{ of } x = x + \frac{44}{900}x = x \left(1 + \frac{44}{900}\right) = x \left(\frac{944}{900}\right) \]
Thus, the new SP becomes:
\[ \text{New SP} = \frac{944}{900}x \]

### Step 5: Calculate the new profit
The new profit is given to be three times the initial profit:
\[ \text{New Profit} = \text{New SP} - CP = \frac{944}{900}x - 2800 \]
Setting this equal to three times the initial profit:
\[ \frac{944}{900}x - 2800 = 3(x - 2800) \]

### Step 6: Solve the equation
Expanding the right side:
\[ \frac{944}{900}x - 2800 = 3x - 8400 \]
Rearranging gives:
\[ \frac{944}{900}x - 3x = -8400 + 2800 \]
This simplifies to:
\[ \frac{944}{900}x - \frac{2700}{900}x = -5600 \]
Combining terms:
\[ \frac{944 - 2700}{900}x = -5600 \]
This leads to:
\[ \frac{-1756}{900}x = -5600 \]
Multiplying both sides by -900:
\[ 1756x = 5600 \times 900 \]
Calculating the right side:
\[ 1756x = 5040000 \]
Now, dividing by 1756:
\[ x = \frac{5040000}{1756} = 3600 \]

### Final Answer
The initial selling price (SP) of the chair is Rs. 3600.

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