sarthakaggarwal wrote:
James buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been
A 60
B 50
C 55
D 54
E 65
Solution: Let us assume the MP of each toy \(= x\). So MP for all (12) toys \(= 12x\).
For first \(8\) toys, selling price \(SP= 8x(1-\frac{20}{100})=8x\times 0.8=6.4x\)
Because we know the formula \(SP=MP(1+\frac{d}{100})\)and for rest \(4\) toys, selling price \(SP= 4x(1-\frac{20}{100})(1-\frac{25}{100})=4x\times 0.8\times 0.75=2.4x\)
Because we know the formula \(SP=MP(1+\frac{d_1}{100})(1+\frac{d_2}{100})\)So the total \(SP_T = 6.4x+2.4x=8.8x\).
Let us assume the total cost price of these \(12\) toys \(= y\).
We are told that he makes a \(10\)% profit.
This means we can write \(8.8x=y(1+\frac{10}{100})⇒y=8x\).
Because we know the formula \(SP=CP(1+\frac{p}{100})\)So, total \(CP_T=8x\) and without discount, total \(SP_T = 12x\).
Profit \(= 12x-8x=4x\). And profit % \(= \frac{4x}{8x}\times 100=50\)%.
HEnce the right answer is
Option B.
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