FIA Test Preparation Lecture #8
Mathematics
Algebra, Age Problems, Work Rate, Percentage, Ratio & Arithmetic
Top MCQs with Proper Lecture Notes
1. Basic Arithmetic
Arithmetic means basic calculations: addition, subtraction, multiplication, division, average, percentage, ratio, and simple equations.
Important Formulas
Average = Sum of values ÷ Number of values
Percentage = Part ÷ Total × 100
Profit = Selling Price − Cost Price
Loss = Cost Price − Selling Price
MCQs: Arithmetic
1. 25 + 35 = ?
A) 50
B) 55
C) 60
D) 65
Answer: C) 60
2. 12 × 8 = ?
A) 84
B) 86
C) 96
D) 108
Answer: C) 96
3. 144 ÷ 12 = ?
A) 10
B) 11
C) 12
D) 14
Answer: C) 12
4. Average of 10, 20, 30 is:
A) 10
B) 20
C) 30
D) 40
Answer: B) 20
Reason: 10 + 20 + 30 = 60, 60 ÷ 3 = 20.
5. Average of 5, 7, 9, 11 is:
A) 6
B) 7
C) 8
D) 9
Answer: C) 8
Reason: 5 + 7 + 9 + 11 = 32, 32 ÷ 4 = 8.
2. Algebra
Algebra uses letters like x, y, a, b to represent unknown values.
Basic Rules
If:
x + 5 = 12
then x = 12 − 5 = 7
If:
2x = 10
then x = 10 ÷ 2 = 5
MCQs: Algebra
6. If x + 4 = 10, then x = ?
A) 4
B) 5
C) 6
D) 7
Answer: C) 6
7. If 2x = 18, then x = ?
A) 6
B) 7
C) 8
D) 9
Answer: D) 9
8. If 3x + 2 = 11, then x = ?
A) 2
B) 3
C) 4
D) 5
Answer: B) 3
Reason: 3x = 9, x = 3.
9. If x − 7 = 15, then x = ?
A) 20
B) 21
C) 22
D) 23
Answer: C) 22
10. If 5x = 45, then x = ?
A) 7
B) 8
C) 9
D) 10
Answer: C) 9
11. If x/4 = 6, then x = ?
A) 18
B) 20
C) 22
D) 24
Answer: D) 24
12. If 2x + 5 = 17, then x = ?
A) 5
B) 6
C) 7
D) 8
Answer: B) 6
3. Age Problems
In age problems, present age is usually taken as x.
Method
If Ali’s age is x, then:
After 5 years = x + 5
5 years ago = x − 5
Twice the age = 2x
Three times the age = 3x
MCQs: Age Problems
13. Ali is 5 years older than Bilal. If Bilal is 15, Ali is:
A) 18
B) 19
C) 20
D) 21
Answer: C) 20
14. A father is 3 times as old as his son. If son is 12 years old, father is:
A) 24
B) 30
C) 36
D) 40
Answer: C) 36
15. Ahmad’s age is x. His age after 7 years will be:
A) x − 7
B) x + 7
C) 7x
D) x/7
Answer: B) x + 7
16. Sara is 20 years old. Her age 5 years ago was:
A) 10
B) 15
C) 20
D) 25
Answer: B) 15
17. A man is twice as old as his son. If son is 18, man is:
A) 30
B) 32
C) 36
D) 40
Answer: C) 36
18. The sum of ages of Ali and Bilal is 40. Ali is 25. Bilal is:
A) 10
B) 15
C) 20
D) 25
Answer: B) 15
4. Work Rate Problems
Work rate problems are about how fast people complete work.
Important Formula
If a person completes work in n days, then:
One day work = 1/n
Example:
Ali completes work in 5 days.
Ali’s 1 day work = 1/5
If A and B work together:
Total work per day = A’s one day work + B’s one day work
MCQs: Work Rate
19. If Ali completes a work in 10 days, his one day work is:
A) 1/5
B) 1/10
C) 1/15
D) 1/20
Answer: B) 1/10
20. A can do a work in 5 days and B can do it in 10 days. Together they complete it in:
A) 2 days
B) 3.33 days
C) 5 days
D) 10 days
Answer: B) 3.33 days
Reason: 1/5 + 1/10 = 3/10 work per day.
Time = 10/3 = 3.33 days.
21. A can complete work in 6 days. B can complete same work in 12 days. Together:
A) 2 days
B) 3 days
C) 4 days
D) 5 days
Answer: C) 4 days
Reason: 1/6 + 1/12 = 3/12 = 1/4, so 4 days.
22. If 4 men complete work in 6 days, then total man-days are:
A) 10
B) 18
C) 20
D) 24
Answer: D) 24
23. If 6 men do a job in 8 days, how many days will 12 men take?
A) 2
B) 4
C) 6
D) 8
Answer: B) 4
Reason: More men means less time.
6 × 8 = 48 man-days.
48 ÷ 12 = 4 days.
24. If 10 workers finish work in 12 days, 5 workers will finish it in:
A) 12 days
B) 18 days
C) 20 days
D) 24 days
Answer: D) 24 days
5. Percentage
Percentage means “out of 100”.
Important Formulas
x% of y = x/100 × y
Percentage increase = Increase ÷ Original × 100
Percentage decrease = Decrease ÷ Original × 100
MCQs: Percentage
25. 10% of 200 is:
A) 10
B) 15
C) 20
D) 25
Answer: C) 20
26. 25% of 80 is:
A) 10
B) 15
C) 20
D) 25
Answer: C) 20
27. 50% of 90 is:
A) 35
B) 40
C) 45
D) 50
Answer: C) 45
28. 20% of 150 is:
A) 20
B) 25
C) 30
D) 35
Answer: C) 30
29. If price increases from 100 to 120, percentage increase is:
A) 10%
B) 15%
C) 20%
D) 25%
Answer: C) 20%
30. If price decreases from 200 to 150, percentage decrease is:
A) 20%
B) 25%
C) 30%
D) 35%
Answer: B) 25%
Reason: Decrease = 50.
50/200 × 100 = 25%.
31. A student gets 45 marks out of 50. Percentage is:
A) 80%
B) 85%
C) 90%
D) 95%
Answer: C) 90%
32. 15% of 300 is:
A) 35
B) 40
C) 45
D) 50
Answer: C) 45
6. Ratio and Proportion
Ratio is comparison between two quantities.
Example:
2:3 means first quantity is 2 parts and second is 3 parts.
Important Rule
If ratio is a:b and total is given:
First part = a/(a+b) × total
Second part = b/(a+b) × total
MCQs: Ratio
33. Ratio of 2 to 4 is:
A) 1:2
B) 2:1
C) 3:2
D) 4:1
Answer: A) 1:2
34. Simplify 10:20.
A) 1:2
B) 2:1
C) 3:4
D) 5:2
Answer: A) 1:2
35. Divide 60 in ratio 2:3. First part is:
A) 20
B) 24
C) 30
D) 36
Answer: B) 24
Reason: 2/(2+3) × 60 = 24.
36. Divide 80 in ratio 3:5. Second part is:
A) 20
B) 30
C) 40
D) 50
Answer: D) 50
Reason: 5/8 × 80 = 50.
37. If a:b = 2:5 and total is 70, value of b is:
A) 20
B) 30
C) 40
D) 50
Answer: D) 50
38. Ratio of 15 and 25 is:
A) 3:5
B) 5:3
C) 2:5
D) 5:2
Answer: A) 3:5
7. Profit and Loss
Formulas
Profit = Selling Price − Cost Price
Loss = Cost Price − Selling Price
Profit % = Profit ÷ Cost Price × 100
Loss % = Loss ÷ Cost Price × 100
MCQs: Profit and Loss
39. Cost price is 100 and selling price is 120. Profit is:
A) 10
B) 15
C) 20
D) 25
Answer: C) 20
40. Cost price is 200 and selling price is 150. Loss is:
A) 25
B) 40
C) 50
D) 60
Answer: C) 50
41. CP = 100, SP = 125. Profit percentage is:
A) 15%
B) 20%
C) 25%
D) 30%
Answer: C) 25%
42. CP = 500, SP = 450. Loss percentage is:
A) 5%
B) 10%
C) 15%
D) 20%
Answer: B) 10%
8. Mixed Important MCQs
43. 3/4 of 100 is:
A) 50
B) 60
C) 75
D) 80
Answer: C) 75
44. 0.5 is equal to:
A) 5%
B) 25%
C) 50%
D) 75%
Answer: C) 50%
45. 1/4 is equal to:
A) 10%
B) 20%
C) 25%
D) 40%
Answer: C) 25%
46. If 5 pens cost Rs. 50, then 1 pen costs:
A) Rs. 5
B) Rs. 10
C) Rs. 15
D) Rs. 20
Answer: B) Rs. 10
47. If 1 dozen = 12, then 5 dozen =:
A) 50
B) 55
C) 60
D) 65
Answer: C) 60
48. Square of 12 is:
A) 124
B) 132
C) 144
D) 156
Answer: C) 144
49. Cube of 3 is:
A) 6
B) 9
C) 18
D) 27
Answer: D) 27
50. If x = 5, then 2x + 3 = ?
A) 10
B) 11
C) 13
D) 15
Answer: C) 13
Quick Revision Table
| Topic | Key Formula |
|---|---|
| Average | Sum ÷ Number |
| Percentage | Part ÷ Total × 100 |
| x% of y | x/100 × y |
| Profit | SP − CP |
| Loss | CP − SP |
| Profit % | Profit ÷ CP × 100 |
| Ratio Part | Given part ÷ Total parts × Total |
| Work | 1 day work = 1/Total days |
Common Mistakes
| Wrong Approach | Correct Approach |
|---|---|
| Adding ages when question asks difference | Read carefully: sum or difference |
| Using SP in profit percentage | Profit % is calculated on CP |
| Confusing since and for in time questions | For math duration, use total time clearly |
| In work problems, adding days directly | Add one-day work, not total days |
| In ratio, dividing total equally | Divide according to parts |
Homework MCQs
1. If x + 8 = 20, x = ?
A) 10
B) 11
C) 12
D) 13
Answer: C) 12
2. 30% of 200 is:
A) 40
B) 50
C) 60
D) 70
Answer: C) 60
3. Divide 100 in ratio 2:3. Second part is:
A) 40
B) 50
C) 60
D) 70
Answer: C) 60
4. A can complete work in 4 days. His one-day work is:
A) 1/2
B) 1/3
C) 1/4
D) 1/5
Answer: C) 1/4
5. CP = 300, SP = 360. Profit percentage is:
A) 10%
B) 15%
C) 20%
D) 25%
Answer: C) 20%
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