A shopkeeper marks an article at $\mathbb{P}\mathbf{x}$ and offers a discount of $69%$ on it. He sells it for $\mathbb{P}\mathbf{434}$ after charging VAT of $12%$ on the discounted price. What is the value of $\mathbf{x}$?

Appeared in: Bihar NHM CHO-2025

Explanation

The problem involves a two-step percentage calculation: a discount followed by a tax.
First, calculate the price after the 69% discount, which is 31% (or 0.31) of the marked price (x).
Next, apply the 12% VAT to this new discounted price. This is equivalent to multiplying the discounted price by 1.12.
The final equation is (0.31 * x) * 1.12 = 434.
Solving for x gives 434 / (0.31 * 1.12) = 434 / 0.3472, which equals 1250.

Option A: If the marked price was ₹1300, the final selling price after a 69% discount and 12% VAT would be (1300 * 0.31) * 1.12 = ₹451.36, not ₹434.
Option B: If the marked price was ₹1200, the final selling price after a 69% discount and 12% VAT would be (1200 * 0.31) * 1.12 = ₹416.64, not ₹434.
Option D: If the marked price was ₹1400, the final selling price after a 69% discount and 12% VAT would be (1400 * 0.31) * 1.12 = ₹486.08, not ₹434.

Visual 1: Flowchart - A flowchart illustrating the sequence of calculations: Start with Marked Price (x) -> Apply 69% Discount -> Get Discounted Price -> Apply 12% VAT -> Arrive at Final Selling Price (₹434). This helps visualize the steps to solve the problem.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Marked Price with Discount and VAT as background academic context rather than a clinical decision trigger.
While not a clinical question, this type of problem tests quantitative aptitude, a key component of the non-nursing section of many nursing entrance and recruitment exams.
Strong analytical and mathematical reasoning skills are essential for interpreting data, calculating medication dosages, and managing resources effectively in a clinical setting.
What if the VAT was applied before the discount? The calculation would change significantly: (x * 1.12) * 0.31 = 434. This would result in a different marked price, highlighting the importance of the order of operations in percentage problems.

How to Approach the Question

Identify the unknown variable, which is the marked price 'x'.
Break down the problem into sequential steps: first the discount, then the tax.
Translate the percentages into decimal form for calculation (e.g., 69% discount means you pay 31% or 0.31; 12% VAT means you multiply by 1.12).
Set up an algebraic equation representing the entire process, equating it to the final given price.
Solve the equation for the unknown variable 'x'.
Alternatively, work backward from the final price: divide by 1.12 to remove the VAT, then divide by 0.31 to remove the discount.

Concept Tested & Keywords

Qk0_kQCVHiuwkwitEogw2-

Practise the full Bihar NHM CHO-2025

Attempt every question from this paper in a timed mock, then review the full solution for each one.