Aman sells two houses at the rate of Rs. 1.995 lakhs each. On one he gains 5% and on the other he loses 5%. His gain or loss percentage in the whole transaction is:

Given:

Selling price of each house = Rs. 1.995 lakhs

Gain on first house = 5%

Loss on second house = 5%

Formula Used:

Cost Price (CP) = Selling Price (SP) / (1 + Gain%)

Cost Price (CP) = Selling Price (SP) / (1 - Loss%)

Loss Percentage = (Total Loss / Total CP) × 100

Calculation:

Let the Cost Price of the first house be CP₁ and the Cost Price of the second house be CP₂.

For the first house: SP = Rs. 1.995 lakhs and Gain = 5%

CP₁ = SP / (1 + Gain%)

CP₁ = 1.995 / (1 + 5/100) = 1.995 / 1.05 = 1.9 lakhs

For the second house: SP = Rs. 1.995 lakhs and Loss = 5%

CP₂ = SP / (1 - Loss%)

CP₂ = 1.995 / (1 - 5/100) = 1.995 / 0.95 = 2.1 lakhs

Total CP = CP₁ + CP₂

Total CP = 1.9 + 2.1 = 4 lakhs

Total SP = 1.995 + 1.995 = 3.99 lakhs

Total Loss = Total CP - Total SP

Total Loss = 4 - 3.99 = 0.01 lakhs

Loss Percentage = (Total Loss / Total CP) × 100

Loss Percentage = (0.01 / 4) × 100

Loss Percentage = 0.25%

The loss percentage in the whole transaction is 0.25%.