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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 average cost price is lower or higher than the selling price is:
  • a)
    10.5% higher
  • b)
    12.5% lower
  • c)
    14.5% lower
  • d)
    8.5% higher
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a local shop as part of promotional measures, the shop owner sells ...
Let SP of each article be Rs. 100.
Thus, C.P of article sold at 13% loss = [100/(100 - 13)] × 100 = (100/87) × 100 = Rs. 115 (approx)
C.P of article sold at 23% profit = [100/(100 + 23)] × 100 = (100/123) × 100 = Rs. 81.3
C.P of article sold at 26% loss = [100/(100 - 26)] × 100 = (100/74) × 100 = Rs. 135.1
Total CP of articles = 115 + 81.3 + 135.1 = Rs. 331.4
Required percentage = [(331.4 - 300)/300] × 100 = 10.5% (Approx)
Average cost price is higher than the average selling price by 10.5% approximately.
Hence, option (a) is correct.
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Most Upvoted Answer
In a local shop as part of promotional measures, the shop owner sells ...
Explanation:

To find the approximate percentage by which the average cost price is lower or higher than the selling price, let's consider the cost price of each variety of soap.

Given:
Loss percentage on the first variety of soap = 13%
Profit percentage on the second variety of soap = 23%
Loss percentage on the third variety of soap = 26%

Calculating the cost price:

Let's assume the selling price of each variety of soap is 'x'.

For the first variety of soap, the cost price can be calculated using the formula:
Cost price = Selling price / (1 - Loss percentage)
So, the cost price of the first variety of soap = x / (1 - 0.13) = x / 0.87

For the second variety of soap, the cost price can be calculated using the formula:
Cost price = Selling price / (1 + Profit percentage)
So, the cost price of the second variety of soap = x / (1 + 0.23) = x / 1.23

For the third variety of soap, the cost price can be calculated using the formula:
Cost price = Selling price / (1 - Loss percentage)
So, the cost price of the third variety of soap = x / (1 - 0.26) = x / 0.74

Calculating the average cost price:

The average cost price can be calculated by taking the average of the cost prices of all three varieties of soap.

Average cost price = (cost price of first variety + cost price of second variety + cost price of third variety) / 3
= (x / 0.87 + x / 1.23 + x / 0.74) / 3
= (1.147x + 0.813x + 1.351x) / 3
= 3.311x / 3
= 1.1037x

Calculating the selling price:

The selling price of each variety of soap is 'x'.

Calculating the percentage difference:

The percentage difference between the average cost price and the selling price can be calculated using the formula:
Percentage difference = (Average cost price - Selling price) / Average cost price * 100

Substituting the values,
Percentage difference = (1.1037x - x) / 1.1037x * 100
= 0.1037x / 1.1037x * 100
= 0.1037 / 1.1037 * 100
≈ 9.4%

Therefore, the approximate percentage by which the average cost price is lower or higher than the selling price is approximately 9.4%.

The correct answer is not 'A' (10.5% higher), but it is approximately 9.4%.
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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 average cost price is lower or higher than the selling price is:a)10.5% higherb)12.5% lowerc)14.5% lowerd)8.5% higherCorrect answer is option 'A'. Can you explain this answer?
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