(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.
(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.
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Correct Answer: Option n
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.
(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.