(a) Madam Kwakyewaa imported a quantity of frozen fish costing GH¢ 400.00. The goods attracted an import duty of 15% of its cost. She also paid a sales tax of 10% of the total cost of the goods including the import duty and then sold the goods for GH¢ 660.00. Calculate the percentage profit. (b) In a school, there are 1000 boys and a number of girls. The 48% of the total number of students that were successful in an examination was made up of 50%of the boys and 40% of the girls. Find the number of girls in the school.
Explanation
(a) Import duty : \(\frac{15}{100} \times 400 = GH¢ 60.00\) New cost price : GH¢400.00 + GH¢ 60 = GH¢ 460.00 Sales tax : \(\frac{10}{100} \times 460 = GH¢ 46.00\) Total cost price : \(GH¢(460 + 46) = GH¢ 506.00\) Profit = GH¢(660 - 506) = GH¢ 154.00 \(% profit = \frac{154}{506} \times 100%\) = \(30.43%\). (b) Let the number of girls be t. Therefore the total number of students = (1000 + t) students. The number that passed the exam = \(\frac{48}{100} \times (1000 + t)\) = \(0.48(1000 + t)\) \(\implies 0.48(1000 + t) = (\frac{50}{100} \times 1000 + \frac{40}{100} \times t)\) \(0.48(1000 + t) = 500 + 0.4t\) \(480 + 0.48t = 500 + 0.4t \implies 0.48t - 0.4t = 500 - 480\) \(0.08t = 20\) \(t = \frac{20}{0.08} = 250\) There are 250 girls in the school.
