A trader sells wheat at 10% profit and uses weight 10% less than the actual measure. What is his actual percentage gain?

Let the cost price of 1 kg wheat = Rs. 100

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When selling at 10% profit, the selling price per kg = Rs. 110

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The trader uses a weight 10% less than the actual measure.

When a customer asks for 1 kg, the trader gives only 0.9 kg but charges Rs. 110.

The actual cost for 0.9 kg:

Cost = $0.9 \times 100$

Cost = Rs. 90

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Selling Price = Rs. 110

Cost Price = Rs. 90

Profit = $110 - 90$

Profit = Rs. 20

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Profit percentage:

Profit % = $\dfrac{\text{Profit}}{\text{Cost Price}} \times 100$

Profit % = $\dfrac{20}{90} \times 100$

Profit % = $\dfrac{2000}{90}$

Profit % = $22.22\%$

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Using the formula:

Actual Gain % = $\dfrac{100 + \text{Profit \%}}{100 - \text{Weight Loss \%}} \times 100 - 100$

Actual Gain % = $\dfrac{110}{90} \times 100 - 100$

Actual Gain % = $122.22 - 100$

Actual Gain % = $22.22\%$

Therefore, the actual percentage gain is $22.22\%$.