The cash difference between the selling price of an artile at a profit of 8% and 12% is Rs. 3. The ratio of two selling prices is :

Options

A. `27:28`
B. `27:29`
C. `29:31`
D. `27 : 31`

Answer

To solve the problem, we need to find the ratio of the two selling prices (SP1 and SP2) when the cost price (CP) is given. Let's break it down step by step.

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

### Step 2: Calculate Selling Price at 8% Profit
To find the selling price (SP1) at an 8% profit:
- Profit = 8% of CP = 8% of 100 = Rs. 8
- Therefore, SP1 = CP + Profit = 100 + 8 = Rs. 108

### Step 3: Calculate Selling Price at 12% Profit
To find the selling price (SP2) at a 12% profit:
- Profit = 12% of CP = 12% of 100 = Rs. 12
- Therefore, SP2 = CP + Profit = 100 + 12 = Rs. 112

### Step 4: Find the Difference Between Selling Prices
The difference between SP2 and SP1 is:
- Difference = SP2 - SP1 = 112 - 108 = Rs. 4

### Step 5: Set Up the Equation
According to the problem, the cash difference between the selling prices at 8% and 12% profit is Rs. 3. However, we calculated a difference of Rs. 4. This discrepancy indicates that our assumption about the cost price might need adjustment.

### Step 6: Adjust for the Given Difference
Let’s denote the cost price as CP. The selling prices can be expressed as:
- SP1 = CP + 0.08 * CP = 1.08 * CP
- SP2 = CP + 0.12 * CP = 1.12 * CP

The difference in selling prices is given as:
- SP2 - SP1 = 1.12 * CP - 1.08 * CP = 0.04 * CP

Setting this equal to the given difference:
- 0.04 * CP = 3
- CP = 3 / 0.04 = 75

### Step 7: Recalculate Selling Prices with Correct CP
Now that we have the correct CP, we can recalculate the selling prices:
- SP1 = 1.08 * 75 = Rs. 81
- SP2 = 1.12 * 75 = Rs. 84

### Step 8: Find the Ratio of Selling Prices
Now we can find the ratio of SP1 to SP2:
- Ratio = SP1 : SP2 = 81 : 84

To simplify this ratio:
- Divide both numbers by 3:
- Ratio = 27 : 28

### Final Answer
The ratio of the two selling prices is **27 : 28**.

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