A saleable article passes successively in the hands of three traders each trader sold it fur ther at a gain of 25% of the cost price. If the last trader sold it for Rs 250 then what was the cost price for the first trader ?

Options

A. A. Rs 128
B. B. Rs 150
C. C. Rs 192
D. D. Rs 200

Answer

To find the cost price for the first trader, we can follow these steps:

### Step 1: Understand the Selling Price and Gain
Each trader sells the article at a gain of 25% of their cost price. If the last trader sold the article for Rs 250, we need to work backwards to find the cost price for the first trader.

### Step 2: Calculate the Selling Price of the Last Trader
Let the cost price for the last trader be \( CP_3 \). Since the last trader sells the article at a gain of 25%, we can express the selling price as:
\[ SP_3 = CP_3 + 0.25 \times CP_3 = 1.25 \times CP_3 \]
Given that \( SP_3 = 250 \), we can set up the equation:
\[ 1.25 \times CP_3 = 250 \]

### Step 3: Solve for the Cost Price of the Last Trader
To find \( CP_3 \), we can rearrange the equation:
\[ CP_3 = \frac{250}{1.25} = 200 \]

### Step 4: Calculate the Cost Price of the Second Trader
Now, let \( CP_2 \) be the cost price for the second trader. The second trader also sells at a gain of 25%, so:
\[ SP_2 = CP_2 + 0.25 \times CP_2 = 1.25 \times CP_2 \]
Since \( SP_2 = CP_3 = 200 \), we can set up the equation:
\[ 1.25 \times CP_2 = 200 \]

### Step 5: Solve for the Cost Price of the Second Trader
Rearranging gives:
\[ CP_2 = \frac{200}{1.25} = 160 \]

### Step 6: Calculate the Cost Price of the First Trader
Let \( CP_1 \) be the cost price for the first trader. Using the same logic:
\[ SP_1 = CP_1 + 0.25 \times CP_1 = 1.25 \times CP_1 \]
Since \( SP_1 = CP_2 = 160 \), we can set up the equation:
\[ 1.25 \times CP_1 = 160 \]

### Step 7: Solve for the Cost Price of the First Trader
Rearranging gives:
\[ CP_1 = \frac{160}{1.25} = 128 \]

### Conclusion
The cost price for the first trader is Rs 128.

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