A man sold a horse at a loss of 42.84%. How much percent should he gain in the next transaction so as to make an overall gain of 21.42%, if the two horses are bought at the same price?
Question
A man sold a horse at a loss of 42.84%. How much percent should he gain in the next transaction so as to make an overall gain of 21.42%, if the two horses are bought at the same price?
Solution
Let's denote the cost price of each horse as C.
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The man sold the first horse at a loss of 42.84%. This means he sold it for 57.16% of C (100% - 42.84% = 57.16%).
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He wants to make an overall gain of 21.42% on the total cost of the two horses, which is 2C. This means he wants to sell the two horses for a total of 121.42% of 2C, which is 1.2142 * 2C = 2.4284C.
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He has already sold the first horse for 0.5716C. So, he needs to sell the second horse for 2.4284C - 0.5716C = 1.8568C to achieve his overall gain.
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To find out what percentage gain this represents on the cost price of the second horse, we divide 1.8568C by C and multiply by 100% to convert to a percentage. This gives us a gain of 185.68%.
So, the man needs to gain 185.68% on the second transaction to make an overall gain of 21.42%.
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