Rohit sold a bat for Rs. 1400 at a gain of 12%. For how much did he purchase it?

Answer

To find out how much Rohit purchased the bat for, we can follow these steps:

### Step 1: Understand the given information
- Selling Price (SP) = Rs. 1400
- Gain Percentage = 12%

### Step 2: Let the Cost Price (CP) be X
- We will denote the cost price of the bat as X.

### Step 3: Write the formula for Gain
- Gain = Selling Price - Cost Price
- Gain = SP - CP
- Gain = 1400 - X

### Step 4: Express Gain in terms of Cost Price
- We know that Gain Percentage = (Gain / CP) × 100
- Therefore, 12 = (Gain / X) × 100
- Rearranging gives us Gain = (12/100) * X = (12X / 100)

### Step 5: Set the equations equal
- From Step 3 and Step 4, we can set the two expressions for Gain equal to each other:
\[ 1400 - X = \frac{12X}{100} \]

### Step 6: Clear the fraction
- Multiply through by 100 to eliminate the fraction:
\[ 100(1400 - X) = 12X \]
\[ 140000 - 100X = 12X \]

### Step 7: Combine like terms
- Rearranging gives:
\[ 140000 = 12X + 100X \]
\[ 140000 = 112X \]

### Step 8: Solve for X (Cost Price)
- Divide both sides by 112:
\[ X = \frac{140000}{112} \]
\[ X = 1250 \]

### Conclusion
- Therefore, the cost price of the bat is Rs. 1250.

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