# Top 48 CAT Linear Equations Questions With Solutions

CAT linear equations questions come under algebra in the Quantitative aptitude section of CAT. However, in general, linear equation questions in CAT are considered to be of moderate difficulty level. These questions usually involve solving systems of linear equations or finding the equation of a line that passes through given points. To help the aspirants, we provided all the linear equations questions from the previous CAT papers and the detailed video solutions explained by the CAT experts and IIM Alumni. And the best part is you can download these CAT questions for free without signing up.

Practice a good number of problems to improve your problem-solving skills and develop a strategic approach to solve the question from this topic quickly.

## CAT Linear Equations Questions Weightage Over Past 5 Years

 Year Weightage 2022 6 2021 2 2020 7 2019 3 2018 0

## Tips To Solve CAT Linear Equation Questions

• Fundamentals of this concept are useful in solving the questions of the other topics by assuming the unknown values as variables.
• Be careful of silly mistakes in this topic, as that is how students generally lose marks here.
• The number of equations needed to solve the given problem equals the number of variables.
• A linear equation is an equation which gives a straight line when plotted on a graph.
• Linear equations can be of one variable or two variables, or three variables.
• Let a, b, c and d be constants, and x, y and z are variables. A general form of a single variable linear equation is ax+b = 0.
• A general form of two variable linear equation is ax+by = c.
• A general form of three variable linear equation is ax+by+cz = d.

## CAT Linear Equations Formulas PDF

To help CAT aspirants in their preparation, we have made a comprehensive formula PDF containing all the important linear equations that are essential. This PDF includes all the necessary formulas, techniques, and examples required to solve linear equations efficiently. Click on the link below to download the Linear equations formula PDF.

## CAT 2022 Linear Equations questions

#### Question 1

If $$c=\frac{16x}{y}+\frac{49y}{x}$$ for some non-zero real numbers x and y, then c cannot take the value

#### Question 2

In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is

#### Question 3

Let a and b be natural numbers. If $$a^2 + ab + a = 14$$ and $$b^2 + ab + b = 28$$, then $$(2a + b)$$ equals

#### Question 4

The largest real value of a for which the equation $$\mid x + a \mid + \mid x - 1 \mid = 2$$ has an infinite number of solutions for x is

#### Question 5

A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained, is

#### Question 6

For natural numbers x, y, and z, if xy + yz = 19 and yz + xz = 51, then the minimum possible value of xyz is

## CAT 2021 Linear Equations questions

#### Question 1

A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is

#### Question 2

If $$3x+2\mid y\mid+y=7$$ and $$x+\mid x \mid+3y=1$$ then $$x+2y$$ is:

## CAT 2020 Linear Equations questions

#### Question 1

A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

#### Question 2

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

#### Question 3

Let k be a constant. The equations $$kx + y = 3$$ and $$4x + ky = 4$$ have a unique solution if and only if

#### Question 4

In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent ₹ 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent ₹ 450 on rice in April, then how much did he spend on wheat in May?

#### Question 5

If x and y are non-negative integers such that $$x + 9 = z$$, $$y + 1 = z$$ and $$x + y < z + 5$$, then the maximum possible value of $$2x + y$$ equals

#### Question 6

Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is ₹ 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is

#### Question 7

Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

## CAT 2019 Linear Equations questions

#### Question 1

If $$5^x - 3^y = 13438$$ and $$5^{x - 1} + 3^{y + 1} = 9686$$, then x + y equals

#### Question 2

In 2010, a library contained a total of 11500 books in two categories - fiction and nonfiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?

#### Question 3

Let a, b, x, y be real numbers such that $$a^2 + b^2 = 25, x^2 + y^2 = 169$$, and $$ax + by = 65$$. If $$k = ay - bx$$, then

## CAT 2017 Linear Equations questions

#### Question 1

The number of solutions $$(x, y, z)$$ to the equation $$x - y - z = 25$$, where x, y, and z are positive integers such that $$x\leq40,y\leq12$$, and $$z\leq12$$ is

#### Question 2

How many different pairs(a,b) of positive integers are there such that $$a\geq b$$ and $$\frac{1}{a}+\frac{1}{b}=\frac{1}{9}$$?

## CAT 2007 Linear Equations questions

#### Question 1

Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?

#### Question 2

A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?

#### Question 3

The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the nth day of 2007 (n=1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?

## CAT 2006 Linear Equations questions

#### Question 1

When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

#### Question 2

What is the weight of Praja’s luggage?

#### Question 3

What is the free luggage allowance?

## CAT 2005 Linear Equations questions

#### Question 1

A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs. 250 and Rs. 300 per day respectively. In addition, a male operator gets Rs. 15 per call he answers and a female operator gets Rs. 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?

## CAT 2004 Linear Equations questions

#### Question 1

If group B contains 23 questions, then how many questions are there in group C?

#### Question 2

If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group B?

## CAT 2003 Linear Equations questions

#### Question 1

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r $$\neq$$ 0?

x+ 2y - 3z = p

2x + 6y - 11z = q

x - 2y + 7z = r

#### Question 2

A leather factory produces two kinds of bags, standard and deluxe. The profit margin is Rs. 20 on a standard bag and Rs. 30 on a deluxe bag. Every bag must be processed on machine A and on Machine B. The processing times per bag on the two machines are as follows: The total time available on machine A is 700 hours and on machine B is 1250 hours. Among the following production plans, which one meets the machine availability constraints and maximizes the profit?

#### Question 3

A test has 50 questions. A student scores 1 mark for a correct answer, -1/3 for a wrong answer, and -1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than

#### Question 4

How much does R owe to S in Thai Baht?

#### Question 5

How much does M owe to S in US Dollars?

## CAT 2002 Linear Equations questions

#### Question 1

The owner of a local jewellery store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then, and 2 more besides. He escaped with one diamond. How many did he steal originally?

#### Question 2

Mayank, Mirza, Little and Jaspal bought a motorbike for \$60. Mayank paid one-half of the sum of the amounts paid by the other boys. Mirza paid one-third of the sum of the amounts paid by the other boys. Little paid one-fourth of the sum of the amounts paid by the other boys. How much did Jaspal have to pay?

#### Question 3

A car rental agency has the following terms. If a car is rented for 5 hr or less, then, the charge is Rs. 60 per hour or Rs. 12 per kilometre whichever is more. On the other hand, if the car is rented for more than 5 hr, the charge is Rs. 50 per hour or Rs. 7.50 per kilometre whichever is more. Akil rented a car from this agency, drove it for 30 km and ended up playing Rs. 300. For how many hours did he rent the car?

#### Question 4

A piece of string is 40 cm long. It is cut into three pieces. The longest piece is three times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece.

#### Question 5

Three travellers are sitting around a fire, and are about to eat a meal. One of them has 5 small loaves of bread, the second has 3 small loaves of bread. The third has no food, but has 8 coins. He offers to pay for some bread. They agree to share the 8 loaves equally among the three travellers, and the third traveller will pay 8 coins for his share of the 8 loaves. All loaves were the same size. The second traveller (who had 3 loaves) suggests that he will be paid 3 coins, and that the first traveller be paid 5 coins. The first traveller says that he should get more than 5 coins. How much should the first traveller get?

## CAT 2001 Linear Equations questions

#### Question 1

Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for similar reason. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?

#### Question 2

Every 10 years the Indian Government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri.

Chota Hazri has 4,522 fewer males than Mota Hazri.

Mota Hazri has 4,020 more females than males.

Chota Hazri has twice as many females as males.

Chota Hazri has 2,910 fewer females than Mota Hazri.

What is the total number of males in Chota Hazri?

#### Question 3

At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?

#### Question 4

A change-making machine contains one-rupee, two-rupee and five-rupee coins. The total number of coins is 300. The amount is Rs. 960. If the numbers of one-rupee coins and two-rupee coins are interchanged, the value comes down by Rs. 40. The total number of five-rupee coins is

## CAT 2000 Linear Equations questions

#### Question 1

Two full tanks, one shaped like a cylinder and the other like a cone, contain jet fuel. The cylindrical tank holds 500 litres more than the conical tank. After 200 litres of fuel has been pumped out from each tank the cylindrical tank contains twice the amount of fuel in the conical tank. How many litres of fuel did the cylindrical tank have when it was full?

## CAT 1996 Linear Equations questions

#### Question 1

I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What per cent of the total amount paid by me was paid for the pens?

#### Question 2

Out of two-thirds of the total number of basketball matches, a team has won 17 matches and lost 3 of them. What is the maximum number of matches that the team can lose and still win more than three- fourths of the total number of matches, if it is true that no match can end in a tie?

## CAT 1991 Linear Equations questions

#### Question 1

Iqbal dealt some cards to Mushtaq and himself from a full pack of playing cards and laid the rest aside. Iqbal then said to Mushtaq. "If you give me a certain number of your cards, I will have four times as many cards as you will have. If I give you the same number of cards, I will have thrice as many cards as you will have". Of the given choices, which could represent the number of cards with Iqbal?

## CAT 1990 Linear Equations questions

#### Question 1

Consider the following steps :
1. Put x = 1, y = 2
2. Replace x by xy
3. Replace y by y +1
4. If y = 5 then go to step 6 otherwise go to step 5.
5. Go to step 2
6. Stop Then the final value of x equals