A shopkeeper purchased some dresses and pairs of shoes for a total cost of Rs.48,000. The cost of one dress is Rs.400 and the cost of one pair of shoes is Rs.1,000. He sold all the items at a total profit of Rs.18,000. How many dresses and pairs of shoes did he purchase?

1. A

   60 dresses and 10 pairs of shoes

2. B

   70 dresses and 20 pairs of shoes

3. C

   80 dresses and 30 pairs of shoes

4. D

   50 dresses and 25 pairs of shoes

Appeared in: NORCET-11 Prelims

Explanation

• Let the number of dresses be x and pairs of shoes be y.
• Each dress costs Rs.400, each pair of shoes costs Rs.1,000.
• Total cost: 400x + 1000y = 48,000.
• Checking the options: 70 dresses (70 x 400 = 28,000), 20 pairs of shoes (20 x 1,000 = 20,000), total = 48,000.
• This matches the total purchase cost exactly.
• The profit calculation is not needed to determine the quantities, as all items are sold and the purchase cost is the only constraint for this question.

Why Other Options Were Wrong

• Option A: 60 dresses (60 x 400 = 24,000) and 10 pairs of shoes (10 x 1,000 = 10,000) total only 34,000, which is less than the required 48,000.
• Option C: 80 dresses (80 x 400 = 32,000) and 30 pairs of shoes (30 x 1,000 = 30,000) total 62,000, which exceeds the budget.
• Option D: 50 dresses (50 x 400 = 20,000) and 25 pairs of shoes (25 x 1,000 = 25,000) total 45,000, which is less than the required 48,000.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Application of simultaneous equations to solve a cost-based word problem as background academic context rather than a clinical decision trigger.
• Budgeting and cost calculation are essential skills for nurses managing inventory and supplies in healthcare settings.
• What if? - If the cost per dress or shoe changed, the quantities purchased would need to be recalculated to match the total budget.

How to Approach the Question

• Identify the variables and their unit costs from the question.
• Set up the equation for total cost using the given prices.
• Substitute each option into the equation to check which matches the total cost.
• Eliminate options that do not fit the total cost constraint.
• Select the option that exactly matches the total purchase cost.

Concept Tested & Keywords

• Concept Tested: Application of simultaneous equations to solve a cost-based word problem
• Stem keywords: shopkeeper, dresses, pairs of shoes, total cost Rs.48,000, cost per dress Rs.400, cost per pair of shoes Rs.1,000, profit Rs.18,000
• Lead-in keywords: How many, did he purchase

Question ID

Q26ZVKXqysxTG7gZiL8-CJ

Copy ID

Reference Book

E6 Nutrition Kumud Khanna 2e p. 26-28