An item is sold at two successive gains of 30% and 20%. If the final selling price is Rs. 31200, of the item what is the cost price (in Rs.) of the item ?

Options

A. 15000
B. 20000
C. 22250
D. 24000

Answer

To find the cost price of the item sold at two successive gains of 30% and 20%, we can follow these steps:

### Step 1: Calculate the Single Gain Percentage
We have two successive gains:
- First gain (A) = 30%
- Second gain (B) = 20%

To find the total single gain percentage, we can use the formula:
\[ \text{Total Gain} = A + B + \frac{A \times B}{100} \]

Substituting the values:
\[ \text{Total Gain} = 30 + 20 + \frac{30 \times 20}{100} \]
\[ = 30 + 20 + \frac{600}{100} \]
\[ = 30 + 20 + 6 = 56\% \]

### Step 2: Relate Selling Price to Cost Price
Let the cost price be \( CP \). With a gain of 56%, the selling price (SP) can be expressed as:
\[ SP = CP + \text{Gain} \]
\[ SP = CP + 0.56 \times CP = 1.56 \times CP \]

### Step 3: Set Up the Equation
We know the final selling price is Rs. 31,200. Therefore, we can set up the equation:
\[ 1.56 \times CP = 31200 \]

### Step 4: Solve for Cost Price
To find \( CP \), we can rearrange the equation:
\[ CP = \frac{31200}{1.56} \]

Now, performing the division:
\[ CP = 20000 \]

### Conclusion
The cost price of the item is Rs. 20,000.

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