Call UsTips To Solve CAT Percentage
- Fundamentals of this concept are useful in solving the questions of the other topics by assuming the unknown values as variables. Make sure to cover other inter-related concepts of CAT syllabus. All the inter-related concepts need to be covered to have a good foundation in concepts.
- 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.
- If you are confused, enrolling in CAT online coaching will help you a long way.
- 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 Percentage 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.
1. Linear Equations Formulae: Solving Linear Equations
For equations of the form ax + by = c and mx + ny = p, find the LCM of b and n.
Multiply each equation with a constant to make the y term coefficient equal to the LCM. Then subtract equation 2 from equation 1.
2. Linear Equations Formulae: Straight Lines
Equations with 2 variables: Consider two equations ax + by = c and mx + ny = p. Each of these equations represents two lines on the x-y coordinate plane. The solution of these equations is the point of intersection.
If : This means that both the equations have the same slope but different intercepts, and hence are parallel to each other. There is no point of intersection and no solution.
If : They have different slopes and hence must intersect at some point, resulting in a unique solution.
If : The two lines have the same slope and intercept. Hence, they are the same lines. As they have infinite points common between them, there are infinitely many solutions possible.
Question 1.
The rate of increase of the price of sugar is observed to be 2% more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 20 per kg. The inflation rate for the years 1994 and 1995 are expected to be 8% each. The expected price of sugar on January 1, 1996 would be
Question 2.
What strategy will maximize the guaranteed return to Shabnam?
Question 3.
A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is retyped into sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closest to
Question 4.
Thirty percent of the employees of a call centre are males. Ten II. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background. per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background?I. Twenty five per cent of the employees have engineering background.
Question 5.
Prakash should not test if the number of bad widgets in the lot is:
Question 6.
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
If group B contains 23 questions, then how many questions are there in group C?
Question 7.
If there are 120 defective widgets in the lot, Prakash:
Question 8.
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?
Question 9.
If the number of defective widgets in the lot is between 200 and 400, Prakash:
Question 10.
Each question is followed by two statements, A and B. Answer each question using the following instructions:
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Each question is followed by two statements, A and B. Answer each question using the following instructions:
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Zakib spends 30% of his income on his children’s education, 20% B. Supriyo spends more on healthcare than Zakib.on recreation and 10% on healthcare. The corresponding percentages for Supriyo are 40%, 25%, and 13%. Who spends more on children’s education?A. Zakib spends more on recreation than Supriyo.
Question 11.
If Prakash is told that the lot has 160 defective widgets, he should:
Question 12.
A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is
Question 13.
If there are 200 defective widgets in the lot, Prakash:
Question 14.
A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited?
Question 15.
Gopal went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare. If he buys 20 mangoes, then the number of oranges he can buy is
Question 16.
The owner of an art shop conducts his business in the following manner: Every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X%. After one such up-down cycle, the price of a painting decreased by Rs. 441. After a second up-down cycle the painting was sold for Rs. 1,944.81. What was the original price of the painting?
Question 17.
Choose 1 if the question can be answered by using one of the statements alone, but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together, but not by either statement alone.
Choose 4 if the question cannot be answered even by using both statements together.
Choose 1 if the question can be answered by using one of the statements alone, but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together, but not by either statement alone.
Choose 4 if the question cannot be answered even by using both statements together.
Is Country X's GDP higher than country Y's GDP?GDPs of the countries X and Y have grown over the past five years at compounded annual rate of 5% and 6% respectively.Five years ago, GDP of country X was higher than that of country Y.
Question 18.
An outgoing batch of students wants to gift PA system worth Rs. 4200 to their school. If the teachers offer to pay 50% more than the students, and an external benefactor gives three times teachers’ contribution, how much should the teachers donate?
Question 19.
The table below shows the age-wise distribution of the population of Reposia. The number of people aged below 35 years is 400 million.If the ratio of females to males in the ‘below 15 years’ age group is 0.96, then what is the number of females (in millions) in that age group?
Question 20.
Forty per cent of the employees of a certain company are men, and 75% of the men earn more than Rs. 25,000 per year. If 45% of the company’s employees earn more than Rs. 25,000 per year, what fraction of the women employed by the company earn less than or equal to Rs. 25,000 per year?
Question 21.
One bacterium splits into eight bacteria of the next generation. But due to environmental condition only 50% survives and remaining 50% dies after producing next generation. If the seventh generation number is 4,096 million, what is the number in first generation?
Question 22.
Direction: Each question is followed by two statements, I and II. Answer the questions based on the statements and mark the answer as:
Choose 1 – if the question can be answered with the help of any one statement alone but not by the other statement.
Choose 2 – if the question can be answered with the help of either of the statements taken individually.
Choose 3 – if the question can be answered with the help of both statements together.
Choose 4 – if the question cannot be answered even with the help of both statements together.
Direction: Each question is followed by two statements, I and II. Answer the questions based on the statements and mark the answer as:
Choose 1 – if the question can be answered with the help of any one statement alone but not by the other statement.
Choose 2 – if the question can be answered with the help of either of the statements taken individually.
Choose 3 – if the question can be answered with the help of both statements together.
Choose 4 – if the question cannot be answered even with the help of both statements together.
Radha and Rani appeared in an examination. What was the total number of questions? I. Radha and Rani together solved 20% of the paper. II. Radha alone solved 3/5 of the paper solved by Rani.
Question 23.
A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subject has the same maximum marks, in how many subjects did he pass the examination?
Question 24.
A man earns x% on the first Rs. 2,000 and y% on the rest of his income. If he earns Rs. 700 from income of Rs. 4,000 and Rs. 900 from if his income is Rs. 5,000, find x%.
Question 25.
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 26.
Answer the question based on the information given below.
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.
Option A: Invest in a public sector bank. It promises a return of +0.10%
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3%
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%
Answer the question based on the information given below.
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.
Option A: Invest in a public sector bank. It promises a return of +0.10%
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3%
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%
The maximum guaranteed return to Shabnam is:
Question 27.
Answer the question based on the information given below.
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.
Option A: Invest in a public sector bank. It promises a return of +0.10%
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3%
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%
Answer the question based on the information given below.
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.
Option A: Invest in a public sector bank. It promises a return of +0.10%
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3%
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%
What strategy will maximize the guaranteed return to Shabnam?
Question 28.
Each question is followed by two statements, I and II. Answer each question using the following instructions:
Mark (1) if the question can be answered by using statement I alone but not by using statement II alone.
Mark (2) if the question can be answered by using statement II alone but not by using statement I alone.
Mark (3) if the question can be answered by using either of the statements alone.
Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark (5) if the question cannot be answered by using any of the statements.
Thirty percent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background?
I. Twenty five per cent of the employees have engineering background.
II. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background.
Each question is followed by two statements, I and II. Answer each question using the following instructions:
Mark (1) if the question can be answered by using statement I alone but not by using statement II alone.
Mark (2) if the question can be answered by using statement II alone but not by using statement I alone.
Mark (3) if the question can be answered by using either of the statements alone.
Mark (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark (5) if the question cannot be answered by using any of the statements.
Thirty percent of the employees of a call centre are males. Ten per cent of the female employees have an engineering background. What is the percentage of male employees with engineering background?
I. Twenty five per cent of the employees have engineering background.
II. Number of male employees having an engineering background is 20% more than the number of female employees having an engineering background.
Question 29.
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
If group B contains 23 questions, then how many questions are there in group C?
Question 30.
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
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?
Question 31.
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Zakib spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentages for Supriyo are 40%, 25%, and 13%. Who spends more on children’s education?
A. Zakib spends more on recreation than Supriyo.
B. Supriyo spends more on healthcare than Zakib.
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Zakib spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentages for Supriyo are 40%, 25%, and 13%. Who spends more on children’s education?
A. Zakib spends more on recreation than Supriyo.
B. Supriyo spends more on healthcare than Zakib.
Question 32.
At the end of year 1998, Shepard bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year where p > 0 and q > 0. If Shepard had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?
Question 33.
A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is
Question 34.
A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited?
Question 35.
The owner of an art shop conducts his business in the following manner: Every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X%. After one such up-down cycle, the price of a painting decreased by Rs. 441. After a second up-down cycle the painting was sold for Rs. 1,944.81. What was the original price of the painting?
Question 36.
Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together.
Is Country X's GDP higher than country Y's GDP?
A. GDPs of the countries X and Y have grown over the past five years at compounded annual rate of 5% and 6% respectively.
B. Five years ago, GDP of country X was higher than that of country Y.
Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together.
Is Country X's GDP higher than country Y's GDP?
A. GDPs of the countries X and Y have grown over the past five years at compounded annual rate of 5% and 6% respectively.
B. Five years ago, GDP of country X was higher than that of country Y.
Question 37.
The table below shows the age-wise distribution of the population of Reposia. The number of people aged below 35 years is 400 million.
If the ratio of females to males in the ‘below 15 years’ age group is 0.96, then what is the number of females (in millions) in that age group?
The table below shows the age-wise distribution of the population of Reposia. The number of people aged below 35 years is 400 million.
If the ratio of females to males in the ‘below 15 years’ age group is 0.96, then what is the number of females (in millions) in that age group?
Question 38.
The income of Amala is 20% more than that of Bimala and 20% less than that of Kamala. If Kamala's income goes down by 4% and Bimala's goes up by 10%, then the percentage by which Kamala's income would exceed Bimala's is nearest to
Question 39.
On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the book at 10% gain, he gains Rs. 13. What is the cost price of the book in Rupees?
Question 40.
In a class, 60% of the students are girls and the rest are boys. There are 30 more girls than boys. If 68% of the students, including 30 boys, pass an examination, the percentage of the girls who do not pass is
Question 41.
In 2010, a library contained a total of 11500 books in two categories - fiction and non-fiction. 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 42.
In an examination, the score of A was 10% less than that of B, the score of B was 25% more than that of C, and the score of C was 20% less than that of D. If A scored 72, then the score of D was
Question 43.
The salaries of Ramesh, Ganesh and Rajesh were in the ratio 6 : 5 : 7 in 2010, and in the ratio 3 : 4 : 3 in 2015. If Ramesh's salary increased by 25% during 2010-2015, then the percentage increase in Rajesh's salary during this period is closest to
Question 44.
In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?
Question 45.
Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?
Question 46.
Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi's savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59,500, then Ravi's total monthly savings (in Rs) is:
Question 47.
The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is:
Question 48.
Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is
Question 49.
In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to
Question 50.
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 51.
The population of a town in 2020 was 100000. The population decreased by y% from the year 2020 to 2021, and increased by x% from the year 2021 to 2022, where x and y are two natural numbers. If population in 2022 was greater than the population in 2020 and the difference between x and y is 10, then the lowest possible population of the town in 2021 was
Question 52.
A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is
Question 53.
In an election, there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1 : 2 : 3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was:
Question 54.
Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to
Question 55.
Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is
Question 56.
In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, their overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be
Question 57.
The total of male and female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female populations in the city from 1970 to 1990 is
Question 58.
In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to
Question 59.
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 60.
In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is
Question 61.
