Ratio

9 Grade 7 Mathematics questions on Ratio, with worked marking schemes. 9 questions are available on this topic in full.

1. Question 1

   2 marks

   The ratio of boys to girls is 5:3. If there are 120 pupils, find the number of boys.

   (2 marks)

   Marking scheme

   The ratio $5:3$ gives $5+3=8$ parts altogether, so boys are $\frac{5}{8}$ of the class. (1)

   $\frac{5}{8}\times 120=75$. (1)

   Final answer: $75$ boys. Check: girls $=\frac{3}{8}\times 120=45$, and $75+45=120$.

2. Question 2

   1 mark

   Simplify 45:60.

   A. 5:6

   B. 15:20

   C. 9:12

   D. 3:4

   (1 mark)

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3. Question 3

   4 marks

   A shopkeeper bought 50 oranges at Ksh 8 each. He sold them at Ksh 12 each.

   (a) Find the total cost price. (1 mark)

   (b) Find the total selling price. (1 mark)

   (c) Calculate the percentage profit. (2 marks)

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4. Question 4

   1 mark

   Increase 300 in the ratio 7:5.

   A. 214

   B. 350

   C. 420

   D. 500

   (1 mark)

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5. Question 5

   4 marks

   A shopkeeper bought 50 oranges at Ksh 8 each. He sold them at Ksh 12 each.

   (a) Find the total cost price. (1 mark)

   (b) Find the total selling price. (1 mark)

   (c) Calculate the percentage profit. (2 marks)

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6. Question 6

   2 marks

   Mixtures A and B are in the ratio 3:5. If mixture A is 450 ml, find mixture B.

   (2 marks)

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7. Question 7

   4 marks

   Three workers share profit in ratio 2:3:5. Total profit is Ksh 150,000. How much does each get?

   (4 marks)

   Marking scheme

   The ratio $2:3:5$ gives $2+3+5=10$ parts in total, so each worker takes that fraction of the profit. (1)

   First worker: $\frac{2}{10}\times 150,000=30,000$. (1)

   Second worker: $\frac{3}{10}\times 150,000=45,000$. (1)

   Third worker: $\frac{5}{10}\times 150,000=75,000$. Check: $30,000+45,000+75,000=150,000$. (1)

   Final answer: Ksh $30,000$, Ksh $45,000$ and Ksh $75,000$.

8. Question 8

   1 mark

   Divide 720 in the ratio 2:3:4.

   A. 180, 240, 300

   B. 120, 240, 360

   C. 160, 240, 320

   D. 240, 240, 240

   (1 mark)

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9. Question 9

   1 mark

   A map scale is 1:25,000. A distance of 8 cm on the map represents:

   A. 200 km

   B. 2 km

   C. 200 m

   D. 20 km

   (1 mark)

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