D sells a table to E at a profit of 30% and E sells it to F at a loss of 30%. What is the ratio of cost prices of D and F?

Options

A. `100:91`
B. `100:130`
C. `100:126`
D. `1:1`

Answer

To solve the problem step by step, we will follow the transactions between D, E, and F.

### Step 1: Assume the Cost Price of D
Let's assume the cost price (CP) of D is Rs 100.

### Step 2: Calculate the Selling Price of D to E
D sells the table to E at a profit of 30%.
- Profit = 30% of CP of D = 30% of 100 = Rs 30.
- Selling Price (SP) of D = CP of D + Profit = 100 + 30 = Rs 130.

### Step 3: Calculate the Cost Price of E
The cost price of E is the same as the selling price of D, which is Rs 130.

### Step 4: Calculate the Selling Price of E to F
E sells the table to F at a loss of 30%.
- Loss = 30% of CP of E = 30% of 130 = Rs 39.
- Selling Price (SP) of E = CP of E - Loss = 130 - 39 = Rs 91.

### Step 5: Calculate the Cost Price of F
The cost price of F is Rs 91, which is the selling price of E.

### Step 6: Find the Ratio of Cost Prices of D and F
Now, we need to find the ratio of the cost price of D to the cost price of F.
- CP of D = Rs 100
- CP of F = Rs 91

The ratio of CP of D to CP of F is:
\[ \text{Ratio} = \frac{\text{CP of D}}{\text{CP of F}} = \frac{100}{91} \]

### Final Answer
The ratio of the cost prices of D and F is 100:91.

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