Harish sold a bicycle at 8% gain. Had it been sold for Rs.375 more, the gain would have been 14%. Find the cost price of the bicycle.

Answer

To solve the problem, we need to find the cost price of the bicycle based on the information given about the selling price and the profit percentages.

Let's denote the cost price of the bicycle as \( x \).

### Step 1: Calculate the selling price at 8% gain
The selling price (SP) when Harish sells the bicycle at an 8% gain can be calculated using the formula:
\[ SP = CP + \text{Gain} \]
Where Gain = \( \frac{8}{100} \times CP \).

So, we can express the selling price as:
\[ SP = x + \frac{8}{100} \times x = x + 0.08x = 1.08x \]

### Step 2: Calculate the selling price at 14% gain
If the bicycle had been sold for Rs. 375 more, the selling price would be:
\[ SP' = SP + 375 = 1.08x + 375 \]
At a 14% gain, the selling price can also be expressed as:
\[ SP' = x + \frac{14}{100} \times x = x + 0.14x = 1.14x \]

### Step 3: Set up the equation
Now we can set the two expressions for the selling price equal to each other:
\[ 1.08x + 375 = 1.14x \]

### Step 4: Solve for x
To solve for \( x \), we will rearrange the equation:
\[ 375 = 1.14x - 1.08x \]
\[ 375 = 0.06x \]
Now, divide both sides by 0.06:
\[ x = \frac{375}{0.06} \]
Calculating this gives:
\[ x = 6250 \]

### Conclusion
The cost price of the bicycle is Rs. 6250.

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