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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