Mastering Linear Equations for CAT: Your Essential Practice Sheet 2

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 If the sum of two numbers be multiplied by each number separately, the products so obtained are 247 and 114. find the sum of the numbers.

a.19

b.20

c.21

d.23

Q.2 A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Find the number of oranges he purchased.

a.36

b.40

c.15

d.20

Q.3 The difference between a three - digit number and the number formed by reversing its digits is 396. The difference of the hundreds and the units digits is one less than the sum of the units and the tens digits. Also, the hundreds digit is twice the units digit. Find the number.  

a.418

b.412

c.612

d.814

Q.4 Natasha was asked to find (4/7)th of a number. She calculated (4/17)th of the number instead and got an answer, which was 840 less than the correct answer. What is the original number?  

a.2600

b.2599

c.2499

d.2737

Q.5 There is a total of 500 families residing in a locality. For a cultural festival, some families donated Rs. 100 each and the remaining families donated Rs. 50 each. If the total money collected is Rs. 44,450, what is the number of families that donated Rs. 50 each?  

a.399

b.389

c.101

d.111

Q.6 Ninety is divided into three parts such that the sum of the first two parts exceeds the sum of the second and the third parts by 18. If the smallest part is 18 and all the three parts are distinct, then the greatest part is?

a.45

b.54

c.63

d.Cannot be determined

Q.7 Rohan has a certain amount of money and Sohan has a certain amount. If Sohan gives Rs. 60 to Rohan, then the amounts with Rohan and Sohan will be the same. If Rohan gives Rs. 30 to Sohan, the amount with Sohan is thrice the amount with Rohan. What is the total amount with Rohan and Sohan?  

a.Rs. 540

b.Rs. 480

c.Rs. 360

d.Rs. 600

Q.8 Ravindra has three times as much money as Aravinda does. If Ravindra gives a quarter of his money to Aravinda, then Aravinda will have Rs.80 less than Ravindra. How much money does Aravinda start with?

a.175

b.155

c.170

d.160

e.165

Q.9 In an entrance test comprising of 100 questions, a student scores 6 marks for every correct answer and loses 2 marks for every wrong answer. If a student attempted 90 questions and scores 356 marks, then the number of questions answered correctly are?

a.67

b.68

c.70

d.71

Q.10 Veer bought 3 notebooks, 6 pens and 10 belts at Rs.110 and Dheer bought 1 notebook, 7 pens and 20 belts at Rs.150. What is the cost of one pen and one notebook?

a.Rs.14

b.Rs.12

c.Rs.10

d.Rs.8

Q.11 The numerator of a fraction is 6 less than its denominator. If the numerator is decreased by 1 and the denominator is increased by 5, then the denominator becomes 4 times the numerator. Find the fraction.

a.4/11

b.5/11

c.3/11

d.2/11

Q.12 P, Q and R have Rs.6000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R.

a.Rs.3000

b.Rs.3600

c.Rs.2400

d.Rs.4000

Q.13 The sum of the digits of a two-digit number is 7. The new number obtained by reversing the digits when increased by 3 becomes 4 times the original number. Find the original number

a.34

b.16

c.25

d.28

Q.14 The present age of Anju is (1/4)th of her father’s present age. Anju’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?

Q.15 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 is

a.36 years

b.30 years

c.40 years

d.None of the above 

Q.16 The difference between the digits of the two digit number is 4. The sum of the number and the number formed by reversing the digits is 110. Find the two digit number.

a.37

b.73

c.48

d.Cannot be determined

Q.17 Sum of a two digit number and the number formed by reversing the digits is 44. The difference of the number and number formed by reversing the digits 27. Find the number.

a.31

b.63

c. 14

d.No solution

Q.18 The two digits of a two-digit number differ by 4. What is the difference between the number and the number formed by reversing its digits? 

a.72

b.54

c.36

d.Cannot be determined

Q.19 The difference between a three-digit number and the number formed by reversing its digits is always divisible by:

a.only 9

b.only 11

c.101

d.99

Q.20 If the first and the last digits of a three-digit number differ by 3, what is the difference between the three digit number and the number formed  by reversing its digits? 

a.99

b.198

c.297

d.396

Q.21 A two-digit number exceeds the sum of the squares of its digits by 10 and the double of product of its digits by 11. Find the number.

a.23

b.27

c.34

d.67

Q.22 Sum of digits of a 2-digit number is 13. If the digits are interchanged then the new number is 27 less then the original number. Find the new number?

a.85

b.76

c.67

d.58

Q.23 A two digit number is four times the sum of its digits. If 27 is added then it becomes seven times the sum of its digits. The two digit number is

a.12

b.24

c.36

d.48

Q.24 A number consists of two digits. The digit in the tens place is twice the digit in the units place. If 18 be subtracted from the number, the digits are reversed. Find the number.

a.2, 4

b.4  2

c.3, 6

d.4, 8

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