Finding Gain or Loss on Selling a Watch

This problem involves calculating the original cost price of the watch using the information from the first sale and then determining the outcome (gain, loss, or no profit/loss) from a second sale at a different price.

Step 1: Calculate the Cost Price (CP) of the Watch

We are told that selling the watch at Rs. 840 results in a loss of 4%. This means the selling price (SP) is 96% of the cost price (CP).

We can represent this relationship with the formula:

\( \text{SP} = \left( \frac{100 - \text{Loss \%}}{100} \right) \times \text{CP} \)

Substituting the given values:

\( 840 = \left( \frac{100 - 4}{100} \right) \times \text{CP} \)

\( 840 = \left( \frac{96}{100} \right) \times \text{CP} \)

Now, we can solve for CP:

\( \text{CP} = \frac{840 \times 100}{96} \)

\( \text{CP} = \frac{84000}{96} \)

Let's perform the division:

\( \text{CP} = 875 \)

So, the cost price of the watch is Rs. 875.

Step 2: Determine Gain or Loss at the New Selling Price

The watch is now sold for Rs. 875. This is the new selling price (New SP).

We need to compare the new selling price with the cost price we just calculated.

• Cost Price (CP) = Rs. 875
• New Selling Price (New SP) = Rs. 875

Comparing the two values:

\( \text{New SP} = \text{CP} \)

\( 875 = 875 \)

When the selling price is exactly equal to the cost price, there is no profit and no loss.

Conclusion

Since the new selling price (Rs. 875) is the same as the calculated cost price (Rs. 875), selling the watch for Rs. 875 results in neither a gain nor a loss.