# A man sells two houses at the rate of rupees 1.95 lacs each. On one, he gains 5% and on the other he lost 5%. Find his gain or loss percent in the whole transaction.

A profit or loss is the difference between the cost price and the selling price. If the cost price is more than the selling price, then the transaction results in a loss, whereas if the selling price is more than the cost price then the transaction results in a profit.

## Answer: A man who sells two houses at the rate of rupees 1.95 lacs each, gaining 5% and on one and loosing 5% on the other faces a loss percent in the whole transaction which is 0.25%.

A profit% or loss% is calculated always on the cost price, that is Profit% or Loss% = (Profit or Loss)/CP × 100

**Explanation:**

For his first house:

Selling price = Rs 1.95 lacs = Rs 1,95,000

Gain% = 5%

Now we know, CP + P% of CP = SP (P% = gain%)

or, CP + 5% of CP = 1,95,000

or, CP + (5/100) × CP = 1,95,000

or, 105CP/100 = 1,95,000

or, CP = 1,95,000 × 100/105

For his second house:

Selling price = Rs 1.95 lacs = Rs 1,95,000

Loss% = 5%

Now we know, CP - L% of CP = SP (L% = Loss%)

or, CP - 5% of CP = 1,95,000

or, CP - (5/100) × CP = 1,95,000

or, 95CP/100 = 1,95,000

or, CP = 1,95,000 × 100/95

For the whole transaction:

Total selling price = Selling price of the first house + selling price of the second house = Rs 1,95,000 + Rs 1,95,000 = Rs 3,90,000

Total cost price = cost price of the first house + cost price of the second house = 1,95,000 × 100/105 + 1,95,000 × 100/95

= 195000 × 100 × (1/105 + 1/95)

= 19500000 × (1/105 + 1/95)

= 19500000 × (19/1995 + 21/1995)

= 19500000 × 40/1995

= 780000000/1995 ≈ 390977.443

Since CP > SP, therefore, the overall transaction resulted in a loss.

Loss% = (CP - SP)/CP × 100

or, Loss% = (390977.443 - 390000)/390977.443 × 100

= 977.443/390977.443 × 100

= 0.002499 × 100 ≈ 0.25%

### Therefore, the loss percent in the whole transaction is 0.25%.

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