Calculation of Profit or Loss Percentage for a Shopkeeper Selling Two Watches

A shopkeeper sold two watches, each for $100. On the first watch, he had a profit of 10%, while on the second watch, he had a loss of 10%. The question is, despite the identical selling price of $100 per watch, what was the shopkeeper's overall profit or loss percentage?

Analysis and Calculation

To determine the overall profit or loss percentage for the shopkeeper, we can analyze the transactions for each watch and then calculate the total profit or loss based on the cost price (CP) and selling price (SP).

Watch 1

- Selling Price (SP) $100

- Profit 10%

- Cost Price (CP) can be calculated as follows:

[text{Profit} text{SP} - text{CP}]

[10 100 - text{CP}]

[0.1 times text{CP} 100 - text{CP}]

[1.1 times text{CP} 100]

[text{CP} frac{100}{1.1} approx 90.91]

Watch 2

- Selling Price (SP) $100

- Loss 10%

- Cost Price (CP) can be calculated as follows:

[text{Loss} text{CP} - text{SP}]

[10 text{CP} - 100]

[0.1 times text{CP} text{CP} - 100]

[1.1 times text{CP} 100]

[text{CP} frac{100}{0.9} approx 111.11]

Calculating Total Cost Price and Total Selling Price

[text{Total Cost Price (CP)} text{CP of Watch 1} text{CP of Watch 2} 90.91 111.11 202.02]

[text{Total Selling Price (SP)} text{SP of Watch 1} text{SP of Watch 2} 100 100 200]

Calculating Overall Profit or Loss

[text{Overall Loss} text{Total CP} - text{Total SP} 202.02 - 200 2.02]

Calculating Loss Percentage

[text{Loss Percentage} frac{text{Overall Loss}}{text{Total CP}} times 100 left(frac{2.02}{202.02}right) times 100 approx 1%]

Thus, the shopkeeper had an overall loss of approximately 1%.

Shortcut for Competitive Exams

For quick calculations in competitive exams, we can use a shortcut provided by others. This shortcut is particularly useful for saving time:

[text{Loss} frac{x^2}{100^2}]

Here, (x) is the common gain or loss percentage. In this case:

[text{Loss} frac{10^2}{100^2} frac{100}{10000} 0.01 1%]

This means that after the transaction, the seller incurs a loss of 1%.

Note

While shortcuts are useful in competitive exams, it is essential to understand the underlying concepts thoroughly for long-term success.