A trader sold a cycle at a loss of 10%. If the selling price had been increased by Rs. 200, There would have been a gain of 6%. The cost price of the cycle is  

A trader sold a cycle at a loss of 10%. If the selling price had been increased by Rs. 200, There would have been a gain of 6%. The cost price of the cycle is

The cost price of the cycle is Rs. 1250.

Let's denote the cost price of the cycle as CP.

Given that the trader sold the cycle at a loss of 10%, it means the selling price (SP) is 90% of the cost price (since SP = CP - Loss).

So, SP = 0.9 * CP.

If the selling price had been increased by Rs. 200, there would have been a gain of 6%. This means the selling price becomes 106% of the cost price.

So, SP + 200 = 1.06 * CP.

Now, we have a system of two equations:

1. SP = 0.9 * CP
2. SP + 200 = 1.06 * CP

We can substitute the value of SP from equation 1 into equation 2:

0.9 * CP + 200 = 1.06 * CP

Now, let's solve for CP:

0.9 * CP + 200 = 1.06 * CP

200 = 1.06 * CP - 0.9 * CP

200 = 0.16 * CP

200 / 0.16 = CP

CP = 1250

So, the cost price of the cycle is Rs. 1250.

Profit Percentage and Loss Percentages

Profit percentage and loss percentage are measures used to assess the financial performance of a business or an investment. Here's how they are calculated:

1. Profit Percentage: Profit percentage is the percentage of profit earned on a particular investment or the sale of goods. It is calculated using the following formula:

   Profit Percentage = (Profit / Cost Price) * 100%

   Where:

   • Profit is the difference between the selling price and the cost price.
   • Cost Price is the price at which an article is purchased or the cost incurred in producing it.

   For example, if an item is bought for $50 and sold for $70, the profit would be $20. So, the profit percentage would be:

   Profit Percentage = (20 / 50) * 100% = 40%

2. Loss Percentage: Loss percentage is the percentage of loss incurred on a particular investment or the sale of goods. It is calculated using the following formula:

   Loss Percentage = (Loss / Cost Price) * 100%

   Where:

   • Loss is the difference between the cost price and the selling price.
   • Cost Price is the price at which an article is purchased or the cost incurred in producing it.

   For example, if an item is bought for $80 and sold for $60, the loss would be $20. So, the loss percentage would be:

   Loss Percentage = (20 / 80) * 100% = 25%

Understanding profit and loss percentages is crucial for businesses to evaluate their financial performance and make informed decisions regarding pricing, production, and investment strategies.