A vendor sells a coconut for Rs 24 and suffers a loss of 24%. If he wants to make a profit of 14% on the cost price instead, at what price (in rupees) should he sell the coconut?

Introduction / Context:
This question is another example of moving from a known loss situation to a required profit situation on the same item. By using the loss information, we deduce the cost price and then use that cost price to find the selling price that would give a desired profit percentage. It is a direct application of profit and loss formulas.

Given Data / Assumptions:

• The coconut is sold for Rs 24 at a loss of 24%.
• The vendor wants instead to gain 14% on the cost price.
• We must find the new selling price to achieve this 14% profit.
• The cost price is the same in both cases.

Concept / Approach:
When there is a loss of 24%, the selling price equals 76% of the cost price because 100% - 24% = 76%. Thus SP1 = 0.76 * CP. From the given SP1, we can find CP by dividing by 0.76. Then, to get a 14% profit, the new selling price SP2 must be CP * 1.14. This two step process, first to recover CP and then to apply a new profit percentage, is standard.

Step-by-Step Solution:
Let CP be the cost price of the coconut.Given loss = 24%, so SP1 = CP * (1 - 24 / 100) = 0.76 * CP.We are told SP1 = Rs 24.So 0.76 * CP = 24, hence CP = 24 / 0.76.CP = 24 / 0.76 ≈ Rs 31.5789.For a profit of 14%, SP2 = CP * (1 + 14 / 100) = 1.14 * CP.SP2 ≈ 1.14 * 31.5789 ≈ Rs 36.Thus the vendor should sell the coconut for Rs 36 to earn a 14% profit.

Verification / Alternative check:
Using an exact fraction approach, 24% loss means SP1 = 76% of CP, so CP = 24 * 100 / 76 = 2400 / 76 = 600 / 19 = about 31.5789. Then SP2 = CP * 114 / 100 = (600 / 19) * 114 / 100 = (600 * 114) / (19 * 100) = 68400 / 1900 = 36 exactly. So there is no rounding error and the exact required selling price is Rs 36.

Why Other Options Are Wrong:
At Rs 28 or Rs 30 or Rs 32, the profit percentage on a cost price of about Rs 31.58 would be far less than 14%, with Rs 28 and Rs 30 still giving losses and Rs 32 giving only a small profit. Only Rs 36 gives exactly 14% profit on the computed cost price.

Common Pitfalls:
Some learners mistakenly compute the new price by simply adding 38 percentage points to the old selling price or by using 24% and 14% directly on Rs 24, which is incorrect. Profit and loss percentages must be applied on cost price, not on previous selling prices. It is essential to recover the cost price first and then apply the new desired profit percentage.

Final Answer:
The vendor should sell the coconut for Rs 36 to earn a 14% profit.