At a 24% discount, the selling price of a washing machine is Rs. 38,000. What will be its selling price if the discount is increased to 40%?

Introduction / Context:
This problem combines the concepts of discount and marked price. We are given the selling price at one discount rate and then asked to find the selling price at a different discount rate. The key is to first recover the marked price of the washing machine, which is the original price before any discount, and then apply the new discount percentage on this marked price to get the new selling price.

Given Data / Assumptions:
Discount rate 1 = 24 percent.
Selling price at 24 percent discount = Rs. 38,000.
Discount rate 2 (new discount) = 40 percent.
We assume the marked price remains the same in both cases.

Concept / Approach:
A discount of 24 percent means that the customer pays 76 percent of the marked price. In decimal form this is 0.76. Therefore, selling price SP1 = marked price MP * 0.76. From this relation we find MP = SP1 / 0.76. Once we know the marked price, we apply the new discount of 40 percent, which leaves 60 percent of the marked price payable. Hence, new selling price SP2 = MP * 0.60. This two step approach is standard whenever we move from one discount rate to another using the same marked price.

Step-by-Step Solution:
Let marked price be MP. At 24 percent discount, payable percentage = 100 percent - 24 percent = 76 percent. So SP1 = 0.76 * MP. We are given SP1 = Rs. 38,000, so 0.76 * MP = 38000. Therefore MP = 38000 / 0.76. Compute 38000 / 0.76 = 50000. Now apply the new discount of 40 percent, so payable percentage = 60 percent, or 0.60. New selling price SP2 = MP * 0.60 = 50000 * 0.60 = 30000. Thus, the selling price at a 40 percent discount will be Rs. 30,000.

Verification / Alternative check:
We can verify by checking the relationship between the two selling prices. When discount rises from 24 percent to 40 percent, the payable fraction reduces from 0.76 to 0.60. The ratio of the new selling price to the old selling price should be 0.60 / 0.76. Compute 0.60 / 0.76 and multiply by 38,000; the result is 30,000. This confirms that the new selling price is consistent with the change in discount percentage and the constant marked price.

Why Other Options Are Wrong:
Rs. 18,000 would correspond to a payable fraction of only 0.36 of the marked price, which matches a 64 percent discount, not 40 percent. Rs. 22,320 and Rs. 31,920 do not align with the exact ratio 0.60 of the computed marked price 50,000. Only Rs. 30,000 is exactly 60 percent of the marked price, which is the correct pay amount at a 40 percent discount.

Common Pitfalls:
Some candidates mistakenly try to adjust the 38,000 directly by 16 percent (the difference between 24 percent and 40 percent), which is incorrect because discount percentages apply to the marked price, not to the selling price. Others may wrongly add or subtract discount percentages as if they were absolute rupee amounts. The safe method is always to first retrieve the marked price using the first discount information and then apply the second discount to that marked price.

Final Answer:
With a 40 percent discount, the washing machine will sell for Rs. 30,000.