A cycle is sold at 20% gain. If it had been sold at 20% loss, the selling price would have been Rs. 120 less. The cost price of the cycle is

Let's solve this step by step:

Step 1: Let's assume the cost price of the cycle is Rs. x.

Step 2: According to the problem, the cycle is sold at a 20% gain. So, the selling price of the cycle would be Rs. x + 20% of x = 1.2x.

Step 3: The problem also states that if the cycle had been sold at a 20% loss, the selling price would have been Rs. 120 less. So, the selling price in this case would be Rs. x - 20% of x = 0.8x.

Step 4: According to the problem, the difference between the selling price at 20% gain and the selling price at 20% loss is Rs. 120. So, we can set up the equation: 1.2x - 0.8x = 120.

Step 5: Solving the equation gives us: 0.4x = 120.

Step 6: To find the value of x, we divide both sides of the equation by 0.4: x = 120 / 0.4 = Rs. 300.

So, the cost price of the cycle is Rs. 300.