Question : Akash sold a motorcycle to Navin at a profit of 10%. Navin sold it to Vinay at a profit of 20%. Vinay sold it to Vishal at a loss of 5%. If Vishal paid INR 62,700 for the motorcycle, then what was the cost of the motorcycle (in INR ) for Akash?
Option 1: 48,000
Option 2: 48,500
Option 3: 52,500
Option 4: 50,000
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Correct Answer: 50,000
Solution :
Here CP denotes cost price and SP denotes selling price.
SP for Vinay = INR 62700
Loss = 5%
CP for Vinay $=\frac{100}{100-\text{Loss}\%}$ × Selling price $= \frac{100}{100-5}×62700=\frac{100}{95}×62700=66000$
SP for Navin = INR 66000
Profit = 20%
CP for Navin $=\frac{100}{100+\text{Profit}\%}$ × Selling price $=\frac{100}{100+20}×66000=\frac{100}{120}×66000=55000$
SP for Akash = INR 55000
Profit = 10%
CP for Akash $=\frac{100}{100+\text{Profit}\%}$ × Selling price $=\frac{100}{100+10}×55000=\frac{100}{110}×55000=50000$
Hence, the correct answer is 50,000.
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