Suraj0184 wrote:
A fruit seller buys 60 oranges and 50 bananas such that price of 5 bananas is equivalent to price of 4 oranges. If he sells equal number of bananas and oranges at the loss of 20 percent and remaining at the profit of 40 percent such that his overall profit is 18.4 percent. What is the total number of oranges and bananas that he sold at profit?
A. 30
B. 40
C. 50
D. 60
E. 70
Let the price be A and B respectively for oranges and banana => Total = 60A+50B
price of 5 bananas is equivalent to price of 4 oranges => 5B = 4A or 50B = 40A
Thus, total cost = 60A+40A = 100A
Now, assume that x be the number of each sold at loss of 20%. => \(0.8(xA+xB) = 0.8x(A+B) = 0.8x(A+\frac{4A}{5}) = 0.8x(\frac{9A}{5})\).
Thus, the remaining sold at 40% profit will mean => \(1.4((60-x)A+(50-x)B)=1.4((60-x)A+(50-x)\frac{4A}{5})=84A-1.4xA+56A-\frac{5.6xA}{5}\)
\(140A-\frac{12.6xA}{5}\)
Total selling price = \(0.8x(\frac{9A}{5})+140A-\frac{12.6xA}{5}=140A-\frac{5.4xA}{5}\)
Overall 18.4% profit means, the selling price was 1.184*100A = 118.4A
Thus, \(140A-\frac{5.4xA}{5}=118.4A\)
\(21.6=\frac{5.4x}{5}.........x=\frac{108}{5.4}=20\)
Number of fruits sold at profit = (60-x)+(50-x) = 40 + 30 = 70
E
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