300+ CAT Arithmetic Questions with Video solutions & Formulas

Arithmetic Questions form a very important part of the CAT Quants section. You can expect around 9-10 questions in the 22-question format of the CAT Quant section. To get more than the 99 percentile in CAT Quant section plays a crucial part.  Comparing the past papers CAT, the scope of Arithmetic Questions appearing has increased from various mixed topics such as Averages, Profit and Loss, Percentages and Simple Interest and Compound interest. So, the candidates must need strong preparation from scratch. This can be achieved by gaining a firm grip on the basic fundamentals of quant and practising as many Arithmetic Questions as possible. Take 3 Free CAT Mock Tests which will help you know where you currently stand, and will help you in analysing your strengths and weaknesses.

Here, we will provide you with top must-practice questions from the arithmetic of CAT quant section. From all the CAT previous years' papers in pdf format with detailed video solutions.These are good sources for CAT preparation. After practising these questions, one can gain more confidence to attempt the Arithmetic questions in the actual CAT examination.

Topics Sub Topics CAT 2023 CAT 2022 CAT 2021
Arithmetic Time, Speed & Distance 5 4 5
Time & Work 3 3 3
Ratio 1 2 0
Simple Interest & Compound Interest 3 3 0
Percentage & Profit & Loss 6 4 5
Averages Mixtures & Allegations 6 10 15

CAT Arithmetic Tips, Tricks & Shortcuts

CAT Arithmetic - Tip 1: Questions based on Arithmetic concepts appear in the CAT and other MBA entrance exams every year. If you're starting the prep, firstly understand the CAT Arithmetic Syllabus; It is the most important topic and hence should not be avoided. Based on our analysis of the Arithmetic CAT Previous Year Questions this was the CAT Arithmetic Weightage: 8-9 questions were asked from Arithmetic.

CAT Arithmetic - Tip 2: CAT Arithmetic Topics include concepts such as Ratios & Proportions, Averages, Mixtures & Alligations, Profit Loss Discount, Simple & Compound Interest, Time Speed Distance, Time & Work, etc. Getting yourself acquainted with the basics of these concepts will help you solve the problems. Learn all the major formulae from these concepts. You can learn all the Important CAT Arithmetic Formulas here.

CAT Arithmetic - Tip 3: In the CAT exam, Arithmetic is Not a very tough quant topic. A strong foundation in this topic will aid a student in answering these questions. Every year more than one-third of the questions are asked from Arithmetic in the CAT Exam.

Comparing the past papers CAT, the scope of Arithmetic Questions appearing has increased from various mixed topics such as Averages, Profit and Loss, Percentages and Simple Interest and Compound interest. So, the candidates must need strong preparation from scratch. This can be achieved by gaining a firm grip on the basic fundamentals of quant and practising as many Arithmetic Questions as possible.

CAT 2023 Arithmetic questions

Question 1

A merchant purchases a cloth at a rate of Rs.100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is

Question 2

A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16 : 9, then the ratio of cocoa in mixture P to that in mixture Q is

Question 3

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, then the time taken, in minutes, by Pipe C to fill the empty tank is

Question 4

Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to

Question 5

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

Question 6

The minor angle between the hours hand and minutes hand of a clock was observed at 8:48 am. The minimum duration, in minutes, after 8.48 am when this angle increases by 50% is

Question 7

Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit made on object A will be nearest to

Question 8

Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

Question 9

Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal amount of milk to make a drink, then the percentage of sugar in this drink will be

Question 10

Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of $$x$$ km till then, where $$x$$ is a whole number and is palindromic, i.e., $$x$$ remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of 26862 km till then, this number again being palindromic. If Brishti never drove at more than 110 km/h, then the greatest possible average speed at which she drove during the trip, in km/h, was

Question 11

Minu purchases a pair of sunglasses at Rs.1000 and sells to Kanu at 20% profit. Then, Kanu sells it back to Minu at 20% loss. Finally, Minu sells the same pair of sunglasses to Tanu. If the total profit made by Minu from all her transactions is Rs.500, then the percentage of profit made by Minu when she sold the pair of sunglasses to Tanu is

Question 12

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

Question 13

There are three persons A, B and C in a room. If a person D joins the room, the average weight of the persons in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2x kg. If the weight of E is 12 kg more than that of D, then the value of x is

Question 14

A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is

Question 15

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the nonmanufacturing employees is

Question 16

The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

Question 17

Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind travelled at a speed of 54 km/h, then the distance, in km, between town A and town B is

Question 18

Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is

Question 19

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs.51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is

Question 20

A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

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