Calculating the Selling Price of a Watch with a Gain

Consider a situation where a man purchases a watch for Rs. 400 and sells it with a gain of 20% of the selling price. How can one determine the selling price of this watch? This article will provide a step-by-step solution to this problem, along with various methods to verify the result.

Step-by-Step Solution

To find the selling price (SP) of the watch, we need to follow a set of logical steps based on the given conditions. The gain in this scenario is 20% of the selling price, and the cost price (CP) is Rs. 400.

Formulating the Equation

We can start by expressing the gain mathematically:

Gain 0.20 × SP

The selling price can also be expressed in terms of the cost price and the gain:

SP CP Gain

Substituting the values, we have:

SP 400 0.20 × SP

Rearranging the equation to isolate SP:

SP - 0.20 × SP 400

0.80 × SP 400

Dividing both sides by 0.80:

SP 400 / 0.80 500

Thus, the selling price of the watch is Rs. 500.

Verifying the Solution

Method 1: Direct Calculation

If we let the selling price of the watch be Rs. 100:

Gain at 20% on selling price 100 - 20 Rs. 80

The cost price of the watch is:

SP - Gain 100 - 80 Rs. 80

When the cost price is Rs. 80, the selling price is Rs. 100. Now we can find the selling price when the cost price is Rs. 440:

Selling price (100 / 80) × 440 Rs. 550

Method 2: Percentage Method

If the cost price is Rs. 100, the gain is Rs. 20, so the selling price would be Rs. 120.

If the cost price is Rs. 1, the gain is Rs. 20/100.

If the cost price is Rs. 440, the gain would be:

Gain (20/100) × 440 Rs. 88

Therefore, the selling price would be:

SP Cost Price Gain 440 88 Rs. 528

However, this result does not match our initial solution, indicating a potential mistake in the calculation process.

Revised Method 2: Percentage Cross-Multiplication

Let the selling price be 10:

Gain 10 - 440 -430, which is incorrect as a negative gain would imply a loss.

Instead, let's use cross-multiplication:

Sp - Gain 440 - 88 352

The correct selling price would then be:

Selling Price (100/80) × 440 Rs. 550

Summary

The selling price of the watch is Rs. 550. This solution aligns with the methods that correctly apply the gain percentage to the cost price.

Conclusion

The problem of determining the selling price when the gain is expressed as a percentage of the selling price is a classic example of proportional reasoning in financial mathematics. By following the steps and methods outlined in this article, one can confidently solve similar problems in the future.