Profit and loss 33 -10th grade

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A deceitful factory owner defrauds 8% in buying and makes a profit of 12 ½ %
from buyer at the time of selling his goods. Find the actual gain percent
of the factory owner.

Solution: Since the factory owner defrauds 8% in buying, so he takes goods
of $108 in exchange of $100

Again, he sells goods of $100 at $(100 + 12 ½) = $(225/2)

By the problem, the factory owner sells goods for $100 at $(225/2)

So, the factory owner sells goods of $1 at ${225/ (2 * 100)}

So, the factory owner sells goods of $108 at ${(225 * 108) / (2 * 100)} = $121 ½

So, the factory owner finally gets $121 ½ in exchange of $100

So, the actual rate of profit = (121 ½ - 100) % = 21 ½ %