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. 18%
• B. 20%
• C. 25%
• D. 30%

Answer 1

Answer: (B)

20%

Answer 2

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

$\text{Profit percentage} = \left( \frac{18.8x}{94x} \right) \times 100 = 20\%$