A cycle was sold at a gain of 10%. Had it been sold for Rs. 260 more, the gain would have been 14% . Find the cost price of cycle.

Answer

To solve the problem step by step, we will denote the cost price of the cycle as \( CP \).

### Step 1: Define the Selling Price at 10% Gain
The selling price (SP) when the cycle is sold at a gain of 10% can be calculated using the formula:
\[ SP = CP + \text{Gain} \]
Since the gain is 10% of the cost price, we can express this as:
\[ SP = CP + 0.10 \times CP = 1.10 \times CP \]

### Step 2: Define the Selling Price at 14% Gain
If the cycle is sold for Rs. 260 more, the selling price becomes:
\[ SP' = SP + 260 \]
At this selling price, the gain is 14%. Therefore, we can express this as:
\[ SP' = CP + 0.14 \times CP = 1.14 \times CP \]

### Step 3: Set Up the Equation
Now we can set the two expressions for the selling price equal to each other:
\[ 1.10 \times CP + 260 = 1.14 \times CP \]

### Step 4: Solve for CP
Rearranging the equation gives:
\[ 260 = 1.14 \times CP - 1.10 \times CP \]
\[ 260 = (1.14 - 1.10) \times CP \]
\[ 260 = 0.04 \times CP \]
Now, divide both sides by 0.04 to find \( CP \):
\[ CP = \frac{260}{0.04} = 6500 \]

### Conclusion
The cost price of the cycle is Rs. 6500.