A shopkeeper sells an item at a profit of 25% and dishonestly uses a weight that is 30% less than the actual weight. Find his total profit %.

Correct option is B

Given:

The shopkeeper sells an item at a profit of 25%.

He dishonestly uses a weight that is 30% less than the actual weight.

Find the total profit percentage.

Formula Used:

Profit % = $$[\frac{(Effective \ Selling\ Price - Cost \ Price) }{ Cost \ Price}] × 100$$%​

In this case, the profit is a combination of actual profit and the gain due to less weight:

Total Profit % = $$[(1 + Actual Profit \%) × (\frac{1 }{ (1 - Decrease \ in \ Weight \%}))] - 1 × 100$$​​

Solution:

Use the formula for Total Profit %.

Given: Actual Profit % = 25% = 0.25, Decrease in Weight = 30% = 0.30

Total Profit % = $$[(1 + 0.25) × (\frac{1 }{ (1 - 0.30)})] - 1 × 100$$​​

= [(1.25) × $$(\frac{1 }{ 0.70})$$​] - 1 × 100

= [1.25 × 1.4286] - 1 × 100

= 1.7857 - 1 × 100

= 0.7857 × 100

= 78.57%

The shopkeeper's total profit percentage is approximately 78.57%.