Question:
A shopkeeper buys 120 red balloons, 80 blue balloons, and 100 green balloons. The cost of 5 red balloons is the same as that of 4 blue balloons or 2 green balloons. He sells all the balloons at a profit of 20% on the total cost price. If he sells 40 red balloons, 30 blue balloons, and 50 green balloons at a discount of 10% on the marked price, and the rest at the marked price, then his overall profit percentage is:
A shopkeeper buys 120 red balloons, 80 blue balloons, and 100 green balloons. The cost of 5 red balloons is the same as that of 4 blue balloons or 2 green balloons. He sells all the balloons at a profit of 20% on the total cost price. If he sells 40 red balloons, 30 blue balloons, and 50 green balloons at a discount of 10% on the marked price, and the rest at the marked price, then his overall profit percentage is:
Updated On: Aug 21, 2024
- 18%
- 20%
- 25%
- 30%
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The Correct Option is B
Solution and Explanation
Let price of 5 red balloons = Price of 4 blue balloons = Price of 2 green balloons = x
Total cost price:
Cost of 120 red balloons = \(\frac{120}{5} \times x = 24x\)
Cost of 80 blue balloons = \(\frac{80}{4} \times x = 20x\)
Cost of 100 green balloons = \(\frac{100}{2} \times x = 50x\)
Total cost price = 24x + 20x + 50x = 94x
Total selling price:
Total number of balloons = 120 + 80 + 100 = 300
Selling price without discount for all balloons =\(1.2 \times 94x = 112.8x\) (since profit is 20% on cost price)
Number of balloons sold at a discount = 40 + 30 + 50 = 120
Selling price of discounted balloons = \(0.9 \times 112.8x = 101.52x\)
Selling price of remaining balloons (without discount) = 112.8x - 101.52x = 11.28x
Total selling price = 101.52x + 11.28x = 112.8x
Overall profit:
Total profit = Total selling price - Total cost price = 112.8x - 94x = 18.8x
\(\text{Profit percentage} = \left( \frac{18.8x}{94x} \right) \times 100 = 20\%\)
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