UNIT – 1

UNIT-I: QUANTITATIVE ABILITY – BASIC MATHEMATICS

Problems on Number system

1. Find the smallest number divisible by both 6 and 8.
2. Which of the following numbers is divisible by 3: 124, 132, 145?
3. Find the largest 3-digit number divisible by 7.
4. Is 3478 divisible by 11?
5. Find a number divisible by 9 between 500 and 600.
6. Is 524 divisible by both 4 and 6?
7. How many 2-digit numbers are divisible by 5?
8. Find the remainder when 12345 is divided by 8.
9. Which of the following numbers is divisible by 12: 144, 156, 170?
10. What is the smallest 4-digit number divisible by 15?
11. 1 Find the unit digit of 347×562
12. What is the unit digit of 2345 ?
13. Find the unit digit of 789×456×321
14. What is the unit digit of (123)3+(456)2
15. What is the unit digit of 1927
16. Find the unit digit of 874×362+529.
17. Find the unit digit of (246)2×(135)3
18. What will the digit in the unit position of (144)132?
23 37 45
19. Determine the digit in the units position of 13 x 27 x 19 ?
20. Find the unit digit of 9876543211.

Problems on Simplification

1. Simplify: 48÷8+15×3−7
A) 54
B) 53
C) 56
D) 55

2. Simplify: 75% of 320+40% of 520

A) 340
B) 345
C) 350
D) 360

3. Simplify: 18+[36÷(12−6)]
A) 24
B) 30
C) 36
D) 48

4. Simplify: 45+12×(6−4)÷2
A) 48
B) 50
C) 60
D) 54

5. Simplify: ¾ +5/6−2/ 3

A) 3/4\
B) 4/5
C) 13/ 12
D) 5/6

6. Simplify: 64÷(16÷4)×3
A) 48
B) 12
C) 64
D) 36

7. Simplify: (25+5×3)−10
A) 30
B) 35
C) 40
D) 45

8. Simplify: 72÷(8+4)+9×2
A) 20
B) 22
C) 24
D) 28

9. Simplify: [15÷5+12]×2
A) 24
B) 28
C) 30
D) 34

10. Simplify: 84÷(14÷7)+5

A) 25
B) 29
C) 35
D) 45

11. What will come in place of ?. (3/8 of 168) x 15 ÷ 5 + ? = 549 ÷ 9 + 235.

A) 189
B)107
C)296
D) None

12.Simplify (0.001344 / 0.3 x 0.7) = ?

A) 0.0064
B) 0.064
C) 0.64
D) 6.4

13.√0.0081 is equal to :

A) 0.09
B) 0.9
C) ±0.08
D) 0.81

14. 0.003 x ?x 0.0003 = 0.00000027

A) 9
B) 3
C) 0.3
D) 0.03
E) None of these

15.64309 - 8703 + 798 - 437 = ?

A) 55606
B) 55697
C) 55967
D) 73373

Problems on Average

1.The average of 5 numbers is 20. If one of the numbers is 25, what is the total of the other 4
numbers?
A) 70
B) 75
C) 80
D) 85

2.The average of 7 consecutive numbers is 23. What is the smallest of these numbers?
A) 19
B) 20
C) 21
D) 22

3. The average age of 10 students is 15 years. A new student aged 20 joins them. What is the
new average?
A) 15.5
B) 16
C) 16.5
D) 17

4. The average of three numbers is 27. If two of the numbers are 24 and 30, what is the third
number?
A) 25
B) 26
C) 27
D) 28

5. The average marks of 50 students is 72. If the marks of one student were incorrectly
recorded as 86 instead of 68, what is the correct average?
A) 71.64
B) 71.84
C) 72
D) 72.32

6. The average weight of 8 people is 60 kg. A person weighing 72 kg leaves the group. What
is the new average weight?
A) 58.5 kg
B) 59 kg
C) 59.5 kg
D) 60 kg

7. The average score of 6 innings is 42. The highest and lowest scores are removed, and the
new average becomes 40. What is the sum of the highest and lowest scores?
A) 22
B) 24
C) 28
D) 32

8.The average of 5 numbers is 50. If one number is excluded, the average becomes 48. What
is the excluded number?
A) 55
B) 56
C) 57
D) 58

9.The average of 10 numbers is 30. If each number is increased by 5, what will be the new
average?
A) 30
B) 35
C) 40
D) 45

10. The average of 12 numbers is 15. If two numbers are added, the new average becomes 16.
What is the sum of the two new numbers?
A) 24
B) 32
C) 40
D) 48

Problems on Ages

1. The present age of a father is three times that of his son. After 5 years, the father’s age will
be twice that of his son. What is the son's current age?
A) 10 years
B) 15 years
C) 20 years
D) 25 years

2. The sum of the ages of a mother and her daughter is 50 years. Ten years ago, the mother’s
age was 4 times her daughter’s age. What is the daughter’s current age?
A) 10 years
B) 12 years
C) 14 years
D) 16 years

3. The ratio of the ages of two friends is 3:4, and the sum of their ages is 28 years. What is
the age of the younger friend?
A) 10 years
B) 12 years
C) 14 years
D) 16 years

4. Five years ago, a man was 6 times as old as his son. Now, he is 4 times as old. What is the
son’s current age?
A) 5 years
B) 10 years
C) 15 years
D) 20 years

5. A man’s age is 125% of his friend’s age, and the friend’s age is 80% of the man’s age. If
their total age is 90 years, what is the man’s age?
A) 50 years
B) 40 years
C) 60 years
D) 45 years
6.The present age of a mother is twice that of her daughter. Eight years ago, the mother’s age
was four times her daughter’s age. What is the mother’s current age?
A) 32 years
B) 36 years
C) 40 years
D) 44 years

7. The ratio of the present ages of two brothers is 4:5. After 5 years, the ratio will be 5:6.
What is the present age of the elder brother?
A) 20 years
B) 25 years
C) 30 years
D) 35 years

8. The average age of a family of 5 members is 30 years. If the age of the youngest member is
10 years, what was the average age of the family at the time of the youngest member’s birth?
A) 20 years
B) 24 years
C) 25 years
D) 28 years

9.Ten years ago, the age of a man was three times that of his son. After 10 years, the man’s
age will be twice that of his son. What is the present age of the son?
A) 10 years
B) 20 years
C) 25 years
D) 30 years

10. The difference between the ages of a mother and her daughter is 21 years. If the mother is
6 times the daughter’s age, what is the daughter’s current age?
A) 3 years
B) 5 years
C) 7 years
D) 9 years

Problems on Percentage

1. Marked Price and Discount

A shopkeeper marks an item at 25% above its cost price and gives a discount of 10% on the
marked price. What is his profit percentage?
A. 12.5%
B. 13.5%
C. 15%
D. 10%

2. Salary Increase and Decrease

The salary of a person is increased by 20% and then decreased by 20%. What is the net
change in salary?
A. 0%
B. 4% decrease
C. 4% increase
D. 10% decrease

3. Population Growth

The population of a town increases by 10% annually. If the current population is 20,000,
what will be the population after 2 years?
A. 22,000
B. 24,200
C. 24,000
D. 22,500

4. Successive Discounts

A product is given two successive discounts of 20% and 10%. What is the net discount
percentage?
A. 28%
B. 30%
C. 32%
D. 25%

5. Profit Percentage

A man buys an article for ₹500 and sells it at 20% profit. What is the selling price?
A. ₹600
B. ₹520
C. ₹580
D. ₹540

6. Ratio of Boys and Girls

In a school, the ratio of boys to girls is 3:2. If 20% of the boys and 25% of the girls are
absent, what percentage of the total students are present?
A. 75%
B. 80%
C. 78%
D. 85%

7. Percentage Increase

The price of a commodity increases from ₹500 to ₹600. What is the percentage increase?
A. 20%
B. 25%
C. 30%
D. 10%

Answer: A. 20%
8. Discounted Price

A product costs ₹2,000 and is sold after a discount of 15%. What is the selling price?
A. ₹1,700
B. ₹1,800
C. ₹1,750
D. ₹1,900

9. Exam Score

A student scores 72 marks in an exam and this is 80% of the total marks. What are the
maximum marks?
A. 90
B. 100
C. 120
D. 150

10. Investment Returns

An investment grows by 10% in the first year and 20% in the second year. What is the overall
percentage increase in the investment after two years?
A. 30%
B. 32%
C. 33%
D. 28%

Problems on Ratio and Proportion

1. Simplifying Ratios

The ratio of 45 minutes to 1.5 hours is:

A. 1:2
B. 2:1
C. 1:3
D. 3:1

2. Distribution of Money

Rs240 is divided among A, B, and C in the ratio 3:4:5. What is C's share?
A. 60
B. 80
C. 100
D. 120

3. Ratio of Ages

The ratio of ages of A and B is 3:5. After 6 years, the ratio becomes 4:5. What is B's current
age?
A. 30 years
B. 24 years
C. 18 years
D. 36 years

4. Mixture Problem

In a mixture of 60 liters, the ratio of milk to water is 2:1. How much water must be added to
make the ratio 1:1?
A. 10 liters
B. 20 liters
C. 30 liters
D. 40 liters

5. Proportions

If x: y= 3:4 and y : z= 5:6 what is x: y: z?

A. 3:5:6
B. 15:20:24
C. 9:12:15
D. 4:5:6

6. Speed Ratio

The speeds of A and B are in the ratio 4:5. If A covers a distance in 40 minutes, how much
time will B take to cover the same distance?
A. 32 minutes
B. 50 minutes
C. 48 minutes
D. 36 minutes

7. Work Distribution

A and B earn in the ratio 2:3. If A earns Rs12,000, how much does B earn?
A. 18,000
B. 20,000
C. 16,000
D. 24,000

8. Mixing Two Solutions

Two solutions have alcohol and water in the ratio 3:2 and 7:3. In what ratio should these
solutions be mixed so that the final mixture has alcohol and water in the ratio 5:3?
A. 1:2
B. 2:1
C. 1:3
D. 3:1

9. Investment Distribution

A invests Rs 5,000, B invests Rs7,500, and C invests Rs10,000 in a business. If they earn a
profit of RS 44,000, what is B’s share?
A. 15,000
B. 14,000
C. 16,000
D. 13,000

10. Sharing Work

A and B can complete a task in the ratio of 3:2. Together, they finish the task in 10 days.
How long will A take to complete the task alone?
A. 15 days
B. 20 days
C. 25 days
D. 30 days