The sale of an item increases by 20% every week. If the difference between the sales of the fourth and the second week is Rs. 1,188, then what is the sale in the third week?

1. A

   Rs 2,160

2. B

   Rs 3,160

3. C

   Rs 2,250

4. D

   Rs 3,240

Appeared in: JSSH Staff Nurse - 2019

Explanation

• The problem describes a weekly sales increase of 20%, which is a geometric progression with a common ratio (r) of 1.2.
• Let the sale in the 2nd week be 'S₂'. The sale in the 4th week will be S₂ × (1.2)² = 1.44 × S₂.
• The given difference is S₄ - S₂ = 1188, which translates to 1.44 × S₂ - S₂ = 1188, or 0.44 × S₂ = 1188.
• Solving for S₂ gives 1188 / 0.44 = Rs. 2,700.
• The sale in the 3rd week (S₃) is S₂ × 1.2, which is 2700 × 1.2 = Rs. 3,240.

Why Other Options Were Wrong

• Option A: This value is incorrect. It might arise from a miscalculation, possibly by incorrectly applying the percentage or mixing up the weeks.
• Option B: This is a calculation error. It does not fit the geometric progression defined by a 20% weekly increase and the given difference.
• Option C: This value represents the sale of the first week, not the third week. If the first week's sale is Rs. 2,250, the third week's sale would be 2,250 × (1.2)² = 2,250 × 1.44 = Rs. 3,240.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Application of Geometric Progression in a word problem involving percentage increase as background academic context rather than a clinical decision trigger.
• This type of question tests quantitative aptitude, a key skill for managing resources, calculating medication dosages, and interpreting data trends in a clinical setting.
• Understanding percentage growth is crucial for tracking epidemiological trends, such as infection rates or patient recovery metrics over time.
• What if the increase was 10% per week? The common ratio would be 1.1. The equation would be (1.1² × S₂) - S₂ = 1188, so 0.21 × S₂ = 1188, making S₂ ≈ 5657. The 3rd-week sale would then be 5657 × 1.1 ≈ Rs. 6,223.

How to Approach the Question

• First, identify the type of progression. A constant percentage increase indicates a geometric progression (GP).
• Determine the common ratio (r). A 20% increase means r = 1 + 20/100 = 1.2.
• Define a variable for an unknown term. It's often easiest to use one of the weeks mentioned in the difference; for example, let the 2nd-week sale be 'x'.
• Express the other terms using the variable and the common ratio (e.g., 4th-week sale = x × r²).
• Formulate an equation based on the information given in the problem (x × r² - x = 1188).
• Solve the equation for the variable 'x' and then use it to calculate the value the question asks for (the 3rd-week sale, which is x × r).

Concept Tested & Keywords

• Concept Tested: Application of Geometric Progression in a word problem involving percentage increase.
• Stem keywords: sale, increases by 20%, every week, difference, fourth week, second week, Rs. 1,188
• Lead-in keywords: what is the sale

Question ID

Q-rlqLUzzztyyNJKIo57AG

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