Numerical Reasoning Test Practice Course: Percentages, percentage change and ratios

1. السؤال 1 من 18

   What is 15% of $240?

   • A$204
   • B$3.60
   • C$36
   • D$16
   أظهر الإجابة

   الإجابة: C. $36

   15% = 0.15. 0.15 × 240 = $36.

2. السؤال 2 من 18

   Of 60 staff, 45 have finished their training. What percentage have finished?

   • A75%
   • B45%
   • C133%
   • D25%
   أظهر الإجابة

   الإجابة: A. 75%

   Part ÷ whole × 100: 45 ÷ 60 × 100 = 75%.

3. السؤال 3 من 18

   A product costs $80. The price goes up by 10%. What is the new price?

   • A$88
   • B$80.80
   • C$8
   • D$90
   أظهر الإجابة

   الإجابة: A. $88

   10% of $80 is $8. New price = 80 + 8 = $88. You can also multiply by 1.10.

4. السؤال 4 من 18

   Weekly orders went from 400 to 460. What is the percentage increase?

   • A60%
   • B115%
   • C13%
   • D15%
   أظهر الإجابة

   الإجابة: D. 15%

   Change ÷ starting value × 100: (460 − 400) ÷ 400 × 100 = 15%. Always divide by the starting (base) value.

5. السؤال 5 من 18

   Overtime fell from 120 hours to 90 hours. What is the percentage decrease?

   • A25%
   • B33.3%
   • C75%
   • D30%
   أظهر الإجابة

   الإجابة: A. 25%

   Decrease ÷ starting value × 100: 30 ÷ 120 × 100 = 25%. 33.3% comes from dividing by the new value.

6. السؤال 6 من 18

   A team has 12 supervisors and 48 other staff. What is the ratio of supervisors to other staff in its simplest form?

   • A12:60
   • B4:1
   • C1:4
   • D1:5
   أظهر الإجابة

   الإجابة: C. 1:4

   12:48. Divide both parts by 12 to get 1:4. Keep the order the question uses: supervisors first.

7. السؤال 7 من 18

   Part-time and full-time staff are in the ratio 3:5. There are 40 staff in total. How many are part-time?

   • A8
   • B24
   • C25
   • D15
   أظهر الإجابة

   الإجابة: D. 15

   3 + 5 = 8 parts. Each part = 40 ÷ 8 = 5 staff. Part-time = 3 × 5 = 15.

8. السؤال 8 من 18

   A $9,000 budget is shared between Team A and Team B in the ratio 2:1. How much does Team A get?

   • A$4,000
   • B$3,000
   • C$6,000
   • D$4,500
   أظهر الإجابة

   الإجابة: C. $6,000

   2 + 1 = 3 parts. One part = 9,000 ÷ 3 = $3,000. Team A gets 2 parts = $6,000.

9. السؤال 9 من 18

   The share of customers who were satisfied rose from 60% to 66%. By how many percentage points did it rise?

   • A6 percentage points
   • B10 percentage points
   • C66 percentage points
   • D1.1 percentage points
   أظهر الإجابة

   الإجابة: A. 6 percentage points

   A change in percentage points is a simple subtraction: 66 − 60 = 6 percentage points.

10. السؤال 10 من 18

    The share of customers who were satisfied rose from 60% to 66%. What is the percentage increase in the satisfaction rate?

    • A6%
    • B10%
    • C9.1%
    • D66%
    أظهر الإجابة

    الإجابة: B. 10%

    Percentage change = change ÷ starting value × 100 = 6 ÷ 60 × 100 = 10%. This is different from the 6-percentage-point rise.

11. السؤال 11 من 18

    After a 25% discount, a jacket costs $60. What was the price before the discount?

    • A$80
    • B$85
    • C$45
    • D$75
    أظهر الإجابة

    الإجابة: A. $80

    After a 25% discount you pay 75% of the price. Original = 60 ÷ 0.75 = $80. Adding 25% to $60 gives $75, which is wrong because 25% was taken from the original price.

12. السؤال 12 من 18

    A bill is $189.00 including 5% tax. What was the amount before tax?

    • A$180.00
    • B$179.55
    • C$198.45
    • D$184.00
    أظهر الإجابة

    الإجابة: A. $180.00

    The bill is 105% of the pre-tax amount. Pre-tax = 189 ÷ 1.05 = $180.00. Taking 5% off $189 gives $179.55, which is wrong.

13. السؤال 13 من 18

    Sales were $5,000 in February. They rose 10% in March, then fell 10% in April. What were April sales?

    • A$4,500
    • B$4,950
    • C$5,000
    • D$5,050
    أظهر الإجابة

    الإجابة: B. $4,950

    March = 5,000 × 1.10 = $5,500. April = 5,500 × 0.90 = $4,950. The 10% fall is taken from the bigger March figure, so you do not get back to $5,000.

14. السؤال 14 من 18

    The table shows new customers by region last month. What percentage of all new customers came from the South region?

    المنطقة	New customers
    North	120
    South	180
    East	150
    West	50

    • A56%
    • B36%
    • C64%
    • D18%
    أظهر الإجابة

    الإجابة: B. 36%

    Total = 500. South share = 180 ÷ 500 × 100 = 36%.

15. السؤال 15 من 18

    A cleaning product is mixed 1 part concentrate to 24 parts water. How much concentrate is in 5 litres of mixed solution?

    • A120 mL
    • B2,000 mL
    • C200 mL
    • D208 mL
    أظهر الإجابة

    الإجابة: C. 200 mL

    1 + 24 = 25 parts in total. 5 L = 5,000 mL. One part = 5,000 ÷ 25 = 200 mL of concentrate. Dividing by 24 forgets the concentrate itself is a part.

16. السؤال 16 من 18

    Which store had the largest percentage increase in sales from last year to this year?

    Store	Sales last year	Sales this year
    Store 1	$52,000	$57,200
    Store 2	$80,000	$86,400
    Store 3	$35,000	$38,850
    Store 4	$64,000	$69,760

    • AStore 3
    • BStore 4
    • CStore 1
    • DStore 2
    أظهر الإجابة

    الإجابة: A. Store 3

    Percentage increases: Store 1 10.0%, Store 2 8.0%, Store 3 11.0%, Store 4 9.0%. Store 3 grew fastest, even though Store 2 had the biggest dollar increase.

17. السؤال 17 من 18

    40% of staff are part-time. Of the part-time staff, 25% work weekends. What percentage of ALL staff are part-time weekend workers?

    • A65%
    • B10%
    • C25%
    • D15%
    أظهر الإجابة

    الإجابة: B. 10%

    Take a percentage of a percentage by multiplying: 0.40 × 0.25 = 0.10, which is 10% of all staff.

18. السؤال 18 من 18

    Shop A grew from $200,000 to $220,000 (10%). Shop B grew from $800,000 to $840,000 (5%). What was the percentage growth of the two shops combined?

    • A15.0%
    • B6.0%
    • C5.7%
    • D7.5%
    أظهر الإجابة

    الإجابة: B. 6.0%

    Combine the totals: from $1,000,000 to $1,060,000, a rise of $60,000. 60,000 ÷ 1,000,000 × 100 = 6.0%. A simple average of 10% and 5% ignores that Shop B is much bigger.

لوحة المفاتيح: 1–4 للإجابة، وEnter للسؤال التالي.