Rates, Ratio & Percentages

12 Grade 8 Mathematics questions on Rates, Ratio & Percentages, with worked marking schemes. 12 questions are available on this topic in full.

1. Question 1

   1 mark

   Ksh 3,500 is shared between two people in the ratio 3:4. How much is the larger share?

   A. Ksh 1,500

   B. Ksh 875

   C. Ksh 1,750

   D. Ksh 2,000

   (1 mark)

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2. Question 2

   1 mark

   A trader bought goods for Ksh 800 and sold them for Ksh 920. What was the percentage profit?

   A. 12%

   B. 13%

   C. 15%

   D. 20%

   (1 mark)

   Marking scheme

   C. $15\%$ — the profit is $920-800=120$, and percentage profit is measured against the buying price: $\frac{120}{800}\times 100=15$. Using the selling price as the base would give $13\%$, which is option B.

3. Question 3

   4 marks

   Three workers share a payment of Ksh 18,000 in the ratio 2:3:4. How much does each worker receive?

   (4 marks)

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4. Question 4

   1 mark

   A worker earns Ksh 600 in 8 hours. What is the rate per hour?

   A. Ksh 4,800

   B. Ksh 80

   C. Ksh 75

   D. Ksh 68

   (1 mark)

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5. Question 5

   1 mark

   Express 45 minutes as a percentage of 2 hours.

   A. 22.5%

   B. 37.5%

   C. 45%

   D. 40%

   (1 mark)

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6. Question 6

   1 mark

   The ratio of boys to girls in a class is 5:7. If there are 35 boys, how many girls are there?

   A. 49

   B. 25

   C. 42

   D. 84

   (1 mark)

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7. Question 7

   1 mark

   Increase Ksh 1,500 by 12%.

   A. Ksh 1,620

   B. Ksh 1,512

   C. Ksh 1,680

   D. Ksh 1,800

   (1 mark)

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8. Question 8

   1 mark

   Express $\frac{3}{4}$ as a percentage.

   A. 34%

   B. 75%

   C. 43%

   D. 70%

   (1 mark)

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9. Question 9

   1 mark

   A car travels 240 km in 3 hours. What is its average speed?

   A. 80 km/h

   B. 720 km/h

   C. 60 km/h

   D. 243 km/h

   (1 mark)

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10. Question 10

    3 marks

    In a class of 40 pupils, 15% were absent. How many pupils were present?

    (3 marks)

    Marking scheme

    First find how many were absent: $15\%$ of $40$. (1)

    $\frac{15}{100}\times 40=6$ pupils absent. (1)

    Those present are the rest of the class: $40-6=34$. (1)

    Final answer: $34$ pupils. Check: $34$ is $85\%$ of $40$.

11. Question 11

    3 marks

    A shopkeeper bought a radio for Ksh 2,400 and sold it at a profit of 25%. Calculate the selling price.

    (3 marks)

    Marking scheme

    Profit is worked out on the buying price, so find $25\%$ of Ksh $2,400$. (1)

    $\frac{25}{100}\times 2,400=600$. (1)

    The selling price is the buying price plus the profit: $2,400+600=3,000$. (1)

    Final answer: Ksh $3,000$.

12. Question 12

    1 mark

    Decrease Ksh 2,000 by 15%.

    A. Ksh 1,700

    B. Ksh 300

    C. Ksh 2,300

    D. Ksh 1,850

    (1 mark)

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