Question 111

# In a local shop, as part of promotional measures, the shop owner sells three different varieties of soap, one at a loss of 13 percent, another at a profit of 23 percent and the third one at a loss of 26 percent. Assuming that the shop owner sells all three varieties of soap at the same price, the approximate percentage by which total cost price is lower or higher than the total selling price is

Solution

Let SP of each soap be $$X$$.

Let's calculate Cost Price (CP) of each soap separately.

$$CP_{1} = \frac{100}{100-13}*X = \frac{100X}{87}$$

$$CP_{2} = \frac{100}{100+23}*X = \frac{100X}{123}$$

$$CP_{2} = \frac{100}{100-26}*X = \frac{100X}{74}$$

Total cost price of 3 soaps= $$\frac{100X}{87}+\frac{100X}{123}+\frac{100X}{74}=3.31X$$

Total  selling price of 3 soaps= $$3X$$

Cost price is higher than the selling price by =$$\frac{3.31X-3X}{3X}*100 \approx10.5$$ percent

Therefore, option A is the correct answer.

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