An item was sold for Rs. 2400 after 2 successive discounts of 40 percent and 50 percent. What is the marked price of the item?

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

The problem requires calculating the original price (Marked Price) before two successive discounts were applied.
Let the Marked Price be 'MP'. The Selling Price (SP) is given as Rs. 2400.
The formula for SP after two successive discounts d₁ and d₂ is: SP = MP × (1 - d₁/100) × (1 - d₂/100).
Substituting the given values: 2400 = MP × (1 - 40/100) × (1 - 50/100).
This simplifies to 2400 = MP × (0.60) × (0.50), which is 2400 = MP × 0.30.
Solving for MP gives: MP = 2400 / 0.30 = Rs. 8000.

Option A: If the marked price were Rs. 6000, applying a 40% discount gives Rs. 3600, and a further 50% discount on that gives a final price of Rs. 1800, not Rs. 2400.
Option B: If the marked price were Rs. 7500, applying the successive discounts (effectively multiplying by 0.3) would result in a selling price of Rs. 2250, which is not the given Rs. 2400.
Option D: If the marked price were Rs. 7200, applying the successive discounts (multiplying by 0.3) would result in a selling price of Rs. 2160, not Rs. 2400.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating Marked Price with Successive Discounts as background academic context rather than a clinical decision trigger.
This is a general aptitude question testing mathematical skills, specifically the application of percentages and discounts.
While not directly clinical, strong numerical literacy is essential for nurses in various tasks such as medication dosage calculations, interpreting lab results, and managing fluid balances.
What if the discounts were applied sequentially on the original marked price instead of successively? The total discount would be 40% + 50% = 90%. The selling price would be 10% of MP. Then MP = 2400 / 0.10 = Rs. 24,000. This highlights the importance of understanding the term 'successive'.

How to Approach the Question

First, identify the key information provided: the final Selling Price (SP = Rs. 2400) and the two successive discount percentages (d₁ = 40%, d₂ = 50%).
Understand that 'successive discounts' means the second discount is applied to the price remaining after the first discount, not on the original price.
Recall the formula that connects Marked Price (MP) and SP with successive discounts: SP = MP × (1 - d₁/100) × (1 - d₂/100).
Rearrange this formula to solve for the unknown variable, which is MP: MP = SP / [(1 - d₁/100) × (1 - d₂/100)].
Substitute the given values into the formula: MP = 2400 / [(1 - 0.40) × (1 - 0.50)].
Perform the calculation: MP = 2400 / (0.60 × 0.50) = 2400 / 0.30 = 8000.

Concept Tested & Keywords

Concept Tested: Calculating Marked Price with Successive Discounts
Stem keywords: sold for, Rs. 2400, successive discounts, 40 percent, 50 percent, marked price
Lead-in keywords: What is

Qu97yxe0T51LzrCkRGEDj

Practise the full DSSSB - 29 August 2019 (Shift-2)

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