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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 prot 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 soap be X.
Let's calculate Cost Price (CP) of each soap separately.
Total cost price of 3 soaps = 
Total  selling price of 3 soaps= 3X
Cost price is higher than the selling price by = 
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Most Upvoted Answer
In a local shop, as part of promotional measures, the shop owner sells...
Calculation of Cost Price and Selling Price for each variety of soap

Let the cost price of each variety of soap be x.

For the first variety, selling price = 87% of x (as it is sold at a loss of 13%)
For the second variety, selling price = 123% of x (as it is sold at a profit of 23%)
For the third variety, selling price = 74% of x (as it is sold at a loss of 26%)

As all three varieties are sold at the same price, let the common selling price be y.

Equating each variety’s selling price to y, we get:
87% of x = y
123% of x = y
74% of x = y

Solving the above equations, we get:
x = y/(87/100) = 1.1494y
x = y/(123/100) = 0.8130y
x = y/(74/100) = 1.3514y

Calculation of Average Cost Price and Selling Price

Let the shop owner buy 100 units of each variety of soap. Then, the cost price of 100 units of each variety would be:
For the first variety, cost price = 100x = 114.94y
For the second variety, cost price = 100x = 81.30y
For the third variety, cost price = 100x = 135.14y

Total cost price of 300 units of soap = 114.94y + 81.30y + 135.14y = 331.38y

Average cost price per unit of soap = Total cost price / Total number of units = 331.38y / 300 = 1.1046y

Since all three varieties are sold at the same price, the selling price per unit of soap = y.

Percentage by which average cost price is lower or higher than the selling price
= [(Selling Price – Average Cost Price) / Average Cost Price] x 100%
= [(y – 1.1046y) / 1.1046y] x 100%
= 10.5% higher

Therefore, the correct answer is option A, 10.5% higher.
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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 prot 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 isa)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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