When a shirt was sold at discount of 20% a person gets profit of 87.5% due to some reason C.P. was increased by 25% and M.P. by Rs 500 and discount offered also increased 25% and person gains the same profit . Find final S.P. ?

Answer

To solve the problem step by step, we will define the variables and use the information given in the question.

### Step 1: Define Variables
Let the initial Marked Price (M.P.) of the shirt be \( x \).

### Step 2: Calculate Initial Selling Price (S.P.)
The shirt is sold at a discount of 20%. Therefore, the Selling Price (S.P.) after the discount is:
\[ \text{S.P.} = \text{M.P.} - \text{Discount} = x - 0.2x = 0.8x \]

### Step 3: Relate S.P. to Cost Price (C.P.)
The profit earned is 87.5%. This means the Selling Price is 187.5% of the Cost Price. Thus, we can express this as:
\[ 0.8x = 1.875 \times \text{C.P.} \]
Let C.P. be \( \text{C.P.} = c \). Therefore:
\[ 0.8x = 1.875c \]
From this, we can express C.P. in terms of M.P.:
\[ c = \frac{0.8x}{1.875} = \frac{32x}{75} \]

### Step 4: Calculate New C.P. and M.P.
According to the question, the C.P. is increased by 25%. So, the new C.P. becomes:
\[ \text{New C.P.} = c + 0.25c = 1.25c = 1.25 \times \frac{32x}{75} = \frac{40x}{75} \]

The M.P. is increased by Rs 500, so the new M.P. is:
\[ \text{New M.P.} = x + 500 \]

### Step 5: Calculate New Discount
The discount offered also increases by 25%. The new discount is:
\[ \text{New Discount} = 0.2x + 0.25 \times 0.2x = 0.2x + 0.05x = 0.25x \]
Thus, the new Selling Price after the discount is:
\[ \text{New S.P.} = \text{New M.P.} - \text{New Discount} = (x + 500) - 0.25(x + 500) \]
Calculating this gives:
\[ \text{New S.P.} = (x + 500) - 0.25x - 125 = 0.75x + 375 \]

### Step 6: Profit Calculation
The profit remains the same at 87.5%, which means:
\[ \text{New S.P.} = 1.875 \times \text{New C.P.} \]
Substituting the values we have:
\[ 0.75x + 375 = 1.875 \times \frac{40x}{75} \]
Calculating the right side:
\[ 1.875 \times \frac{40x}{75} = \frac{75x}{75} = x \]
Thus, we have:
\[ 0.75x + 375 = x \]

### Step 7: Solve for x
Rearranging gives:
\[ 375 = x - 0.75x = 0.25x \]
So,
\[ x = \frac{375}{0.25} = 1500 \]

### Step 8: Find Final Selling Price
Finally, the Selling Price (S.P.) is:
\[ \text{Final S.P.} = 0.75x + 375 = 0.75(1500) + 375 = 1125 + 375 = 1500 \]

### Final Answer
The final Selling Price (S.P.) is **Rs 1500**.

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