Mastering Linear Equations for CAT: Your Essential Practice Sheet 1

Welcome, fellow CAT aspirants!

Linear equations are a cornerstone of the Quantitative Aptitude section of the CAT exam. While they might seem simple, the exam often presents them in complex word problems that test your logical reasoning as much as your mathematical skills. A strong grasp of this topic can significantly boost your score and save you precious time on test day. This blog post provides a comprehensive practice sheet designed to help you tackle these questions with confidence. Inside, you'll find a curated set of problems ranging in difficulty, along with detailed, step-by-step solutions to guide you. Let's get started on building a solid foundation for your CAT preparation!

Q.1 A bag contains a total of 93 coins in the form of one rupee and 50 paise coins. If the total value of coins in the bag is Rs.56, find the number of 50 paise coins in the bag.

a.60

b.56

c.64

d.74

Q.2 The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction.

a.2/3

b.3/5

c.4/7

d.5/9

Q.3 In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 18, find the number.

a.975

b.864

c.684

d.642

Q.4 Three years ago , Anurag was thrice as old as Bhargav was. Two years hence,  Anurag's age will be twice that of Bhargav's age. What is the present age of Anurag? (in years)

a.16

b.18

c.20

d.22

Q.5 Goutam is four times as old as Girija. Four years hence, the age of Goutam will be thrice that of Girija. What is the present age of Goutam (in years)?

a.20

b.24

c.28

d.32

Q.6 The average age of two members of a family is 5 years less than the elder one’s age among the two. What is the difference in the age of the eldest and the youngest among the two persons of the family?

a.5

b.10

c.15

d.Cannot be determined

Q.7 Mudit's age 18 years hence will be thrice his age four years ago. Find Mudit's present age?

a.9 years

b.12 years

c.15 years

d.18 years

Q.8 Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand?

a.14

b.16

c.18

d.20

Q.9 Five years ago, a man was five times as old as his son. Two years hence, the man will be three times as old as his son. What is the present age of the man? (in years) 

a.50 years

b.35 years 

c.42 years 

d.40 years

Q.10 A man’s present age is two – fifth the present age of his mother. After 8 years, he will be half the age of his mother at that time. How old is the mother at present?

a.36 years

b.40 years

c.44 years

d.48 years

e.52 years 

Q.11 The age of a woman is thrice that of her daughter. When the woman was 29 years old, her only son, who is three years younger to her only daughter, was born. What is the present age of her son? 

a.8 years 

b.9 years 

c.10 years 

d.11 years 

Q.12 Three years ago, A’s age was twice that of B’s age. Seven years hence, the sum of their ages will be 83 years. Find the present age of A.

a.45 years

b.50 years

c.52 years

d.54 years

e.56 years 

Q.13 Five years ago, the age of a person was three years more than four times the age of his son. Three years hence, the age of the person will be six years less than thrice the age of his son. After how many years from now will their combined age be 80 years?

a.22

b.20

c.16

d.18

Q.14 The present ages of A, B, C are in the ratio 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages. 

a.22, 34, 42 years

b.20, 32, 40 years

c.14, 26, 34 years

d.18, 30, 38 years

e.16, 28, 36 years

Q.15 If 5x – 3y + 13 = 17 and 15x + 9y = 42, then find the value of 10x – 9y + 3.

a.0

b.1

c.5

d.6

Q.16 A tells B “ When I was 3/5th of your present age you were 5/7th of my present age”. If the present age of A is 28 years, what is the present age of B?

a.20

b.10

c.30

d.Can't be determined

Q.17 Father is four times the age of his daughter. If after 5 years, he would be three times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age?

a.1.5

b.2

c.2.5

d.3

Q.18 The present age of Anju is 1/4th of her father’s present age. Anuj’s father’s age will be twice of Manju’s age after 8 years. If Manju’s tenth birthday was celebrated two years ago then what is Anju’s present age?

a.6 years

b.8 years

c.10 years

d.12 years

e.14 years

Q.19 Find the values of x, y and z.–2x – 6y – 2z = –2;3x + 2y + 5z = 7;–3x – 3y + 3z = 9

a.1, –1, 3

b.2, 0, 1.5

c.0, 2, 3

d.–1, 0, 2

Q.20 The present age of a father is 2 years more than three times the age of his son. Four years hence, father’s age will be 10 years more than twice the age of the son. Find the present age of the father.

32 years

a.34 years

b.36 years

c.38 years

d.40 years 

Q.21 Three oranges, five banannas and two apples cost Rs.40. However four oranges, ten bananas and four apples cost Rs.70. Find the cost of ten oranges.

a.Rs.25

b.Rs.50

c.Rs.30

d.Cannot be determined

Q.22 The sum of the ages of a father and a son is 45 years. Five years ago, the product of their ages was four times the father’s age at that time. The present ages of the father and son respectively are:

a.25 years, 10 years 

b.36 years, 9 years

c.39 years, 6 years

d.52 years, 7 years 

Q.23 10 years ago, the ratio of the ages of A and B was 15 : 11. 5 years hence, the ratio of the ages of A and B will be 5 : 4. What is the present age of B?

a.32 years

b.33 years

c.37 years

d.43 years

e.54 years

Q.24 A number is increased by 5 and then divided by 3, the result is 12. What would be the result if 3 is subtracted from the number and then it is divided by 7?

a.31

b.28

c.14

d.4

Q.25 The cost of three pens, five pencils and two books is Rs. 68. The cost of six pens, seven pencils and four books is Rs. 121. The cost of nine pens, fifteen pencils and six books is Rs. 204. Find the cost of each book.  

a.Rs. 7

b.Rs. 11

c.Rs. 5

d.Cannot be determined

1	2	3	4	5	6	7	8	9	10
D	D	B	B	D	B	C	B	D	B
11	12	13	14	15	16	17	18	19	20
C	A	C	D	D	C	C	B	D	D
21	22	23	24	25
B	B	D	D	D