A sells an article to B at a `20%` profit. B sells it to C at a `15%` loss. C sells it to D at a `25%` profit. If the difference between the profits of A and C is Rs. 49.50 , then the cost price of the article for C is

Options

A. Rs. 918
B. Rs. 900
C. Rs. 954
D. Rs. 909

Answer

To solve the problem step by step, we will break down the transactions and calculate the cost price of the article for C.

### Step 1: Determine the Selling Price of A to B
Let the cost price of the article for A be Rs. P.

A sells the article to B at a 20% profit.
- Profit of A = 20% of P = \(0.2P\)
- Selling Price (SP) of A = Cost Price (CP) + Profit = \(P + 0.2P = 1.2P\)

### Step 2: Determine the Selling Price of B to C
B sells the article to C at a 15% loss.
- Cost Price of B = Selling Price of A = \(1.2P\)
- Loss of B = 15% of \(1.2P = 0.15 \times 1.2P = 0.18P\)
- Selling Price (SP) of B = Cost Price - Loss = \(1.2P - 0.18P = 1.02P\)

### Step 3: Determine the Selling Price of C to D
C sells the article to D at a 25% profit.
- Cost Price of C = Selling Price of B = \(1.02P\)
- Profit of C = 25% of \(1.02P = 0.25 \times 1.02P = 0.255P\)
- Selling Price (SP) of C = Cost Price + Profit = \(1.02P + 0.255P = 1.275P\)

### Step 4: Calculate the Profits of A and C
- Profit of A = \(0.2P\)
- Profit of C = \(0.255P\)

### Step 5: Set Up the Equation for the Difference in Profits
According to the problem, the difference between the profits of A and C is Rs. 49.50.
- Difference = Profit of C - Profit of A = \(0.255P - 0.2P = 0.055P\)
- Set this equal to Rs. 49.50:
\[ 0.055P = 49.50 \]

### Step 6: Solve for P
To find P, divide both sides by 0.055:
\[ P = \frac{49.50}{0.055} = 900 \]

### Step 7: Calculate the Cost Price of the Article for C
Now, we need to find the cost price of the article for C:
\[ \text{CP of C} = 1.02P = 1.02 \times 900 = 918 \]

### Final Answer
The cost price of the article for C is Rs. 918.

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