Question:
Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?
Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?
Updated On: Jul 30, 2025
- 50
- 30
- 25
- 45
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The Correct Option is A
Solution and Explanation
To find out how many dozens of candies Mayank bought, let's set up the equations based on the problem statement:
Let x be the number of dozens of each type of candy that Mayank buys.
Given:
- Cost of first type of candy: ₹15 per dozen
- Cost of second type of candy: ₹12 per dozen
- Selling price for both types of candies: ₹16.50 per dozen
- Total profit: ₹150
Total Cost:
For the first type of candy: x dozens at ₹15 per dozen, total cost = ₹15x
For the second type of candy: x dozens at ₹12 per dozen, total cost = ₹12x
Total cost for both candies = 15x + 12x = ₹27x
Total Revenue:
Both types of candies are sold for ₹16.50 per dozen. Hence, the revenue from selling 2x dozens = ₹16.50(× 2x) = ₹33x
Profit Calculation:
Profit = Revenue - Cost
₹150 = ₹33x - ₹27x
Simplifying gives:
₹150 = ₹6x
Solving for x:
x = 150 / 6 = 25
Therefore, Mayank bought 2x = 2 × 25 = 50 dozens of candies altogether.
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