During a sale, 50% of the goods are sold at 21% profit, 40% of the remaining goods are sold at 36% profit and the still remaining goods are sold at a loss of 29%. If there is an overall profit of x%, then what is the value of x?
9
Take the total value of goods as 100 units (cost price basis).
First part: 50% of goods are sold at 21% profit, contributing a profit of \(0.5 \times 21 = 10.5\).
Remaining goods after the first sale are 50%. Of these, 40% are sold, i.e. \(0.4 \times 50\% = 20\%\) of the total, at 36% profit, contributing \(0.2 \times 36 = 7.2\).
The still remaining goods are \(100\% - 50\% - 20\% = 30\%\), sold at a 29% loss, contributing \(0.3 \times (-29) = -8.7\).
Overall percentage profit \(x = 10.5 + 7.2 - 8.7 = 9\).
Hence, the value of x is 9.
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