1 Work out: (a) 32% of ¥80 D (b) 12.5% of 600 m ...................................................................... D In a school, 57 pupils out of 128 in Year 9 reach level 5 in their Science examination. Express this amount of pupils as a percentage to 1 d.p. 3 A computer costs f900 plus VAT, where VAT is charged at 17(1)/(2)% Find the total cost of the computer. 4 Three students took a History test. (a) Amar got seven -eighths of the questions right. What was his percentage score? 0/0 (b) and a percentage score of 65% What was the maximum possible mark on the test? (c) Was this a higher or a lower mark than Amar? Show your working. Percentages D D D

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1 Work out: (a) 32% of ¥80 D (b) 12.5% of 600 m ...................................................................... D In a school, 57 pupils out of 128 in Year 9 reach level 5 in their Science examination. Express this amount of pupils as a percentage to 1 d.p. 3 A computer costs f900 plus VAT, where VAT is charged at 17(1)/(2)% Find the total cost of the computer. 4 Three students took a History test. (a) Amar got seven -eighths of the questions right. What was his percentage score? 0/0 (b) and a percentage score of 65% What was the maximum possible mark on the test? (c) Was this a higher or a lower mark than Amar? Show your working. Percentages D D D

Answer 1

1a) \(£ 25.6 \) 1b) \(75m\) 2) \(44.5 \%\) 3) \(£ 1057.5 \) 4a) \(87.5\%\) 4b) \( 80 \) 4c) Amar scored higher than Frank as Amar has a overall score of 70 which is higher than Frank's 68.

Answer 2

## Part 1a: To find \(32\%\) of £80, multiply 80 by 0.32 (which is the decimal form of \(32%\)). ### \[n = 80 \times 0.32 \] ## Part 1b: To find \(12.5\%\) of 600m, multiply 600m by 0.125 (which is the decimal form of \(12.5%\)). ### \[ n = 600 \times 0.125 \] ## Part 2: To express the proportion of pupils as a percentage, you need to divide the number of successful students (57) by the total number of students (128) and then multiply by 100. ### \[ \%\text{ of successful students} = \frac{{57}}{{128}}\times 100 \] ## Part 3: The VAT should be incorporated into the cost. First, find the VAT amount by multiplying \( 900 \) by \( \frac{17.5 }{100} \) (the decimal representation of \(17.5\%\)) and add the tariff to the cost. ### \[ \text{VAT} = 900 \times \frac{17.5 }{100} \] ### \[ \text{Total Cost} = \text{Initial Cost} + \text{VAT} \] ## Part 4a: To find Amar's score as a percentage, multiply the fraction \( \frac{7}{8} \) by 100%. ### \[ \text{Amar's Score} = \frac{7}{8} \times 100\% \] ## Part 4b: Since \( 65\% \) represents 52 marks, we can represent the maximum possible score as \(100\% \). To find the complete score, calculate the value of \(100\%\) using simple cross multiplication. ### \[ \frac{52 }{ 65 } = \frac {x}{ 100 } \] ### \[x = \frac{52 \times 100 }{ 65 } \] ## Part 4c: Lastly, find three-eighth of the total marks to compare it with Frank's score. If \( \frac{7}{8}\) equals to Amar's score as a percentage then, find the scores corresponding to \( \frac{7}{8}\) from the total marks calculated before.(It's persuaded because the maximum marks are yet to be identified.) ### \[ \text{Amar's Total Score} = \frac{7}{8} \times \text{Maximum Marks} \] Then manually Austin's total score with Frank's total score(68). # Calculations: ## Step1: \[ n=80\cdot0.32=£25.6 \] ## Step2: \[ n=600\cdot0.125=75m \] ## Step3: \[ \% \text{ of successful students} = 57\div128\cdot100=44.5\% \] ## Step4: \[\text{VAT}=£900\cdot\frac{17.5}{100}=£157.5\] \[\text{Computer plus VAT} = 900 + 157.5 = £1057.5\] ## Step5: \[\text{Amar's score (Raw)}=\frac{7}{8}\cdot100 = 87.5\%\] ## Step6: \[\text{Full Marks} = \frac{(52\cdot100)}{65}=80\] ## Step7: \[\text{Amar's Total Marks} = \frac{7}{8} \cdot 80 = 70\] Then manually: Amar's scores are just slightly above Frank's since 70>68.

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