HomeTestsSearchRankProfile

Percentage Questions

Practice 115 Percentage questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

📚
115
Total Questions
🟢
12
Easy
🟡
101
Medium
🔴
2
Hard

About Percentage — practice questions, PYQs & concepts

Percentage is a frequently-tested topic on Quantitative Aptitude, Quantitative Aptitude@NUM: 57, General Intelligence and Reasoning. ExamTest.live currently lists 115 Percentage questions spanning previous-year papers from 2026 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Percentage weight in competitive exams

Across our Percentage question bank, the largest sources are Quantitative Aptitude (105), Quantitative Aptitude@NUM: 57 (2), General Intelligence and Reasoning (1), Numerical Ability (1) and Quantitative Aptitude@NUM: 55 (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 12 easy Percentage questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Percentage Questions(1100 of 115)

2 pages
Filter:
Q1mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
8% accuracy
If the radius of a sphere is increased by , then what is the percentage (correct to two decimal places) increase in its volume?
Q2mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
8% accuracy
A number is decreased by , then increased by and then further increased by . What is the net increase/decrease percentage in the number (correct to the nearest integer)?
Q3mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
8% accuracy
The histogram represents the percentage of marks scored by a number of students in the class X Board Examination in 2018 in a school. Total number of students = .The number of students who have secured less than of marks is approximately what percentage more than number of students who have secured marks and above?

image
Q4easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
0% accuracy
A invested more than B. B invested less than C, who invested ₹. The total amount invested (in ₹) by all of them together is:
Q5easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
0% accuracy
Two numbers are and , respectively, more than a third number. The ratio of the second number to the first number is:
Q6mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
and are two heavy steel blocks. If is placed on top of , the weight increases by . How much weight will reduce with respect to the total weight of and , if is removed from the top of ?
Q7mediummcqQuantitative AptitudeCompetitive Exam Practice Paper2026
0% accuracy
In an examination, a student who gets of the maximum marks fails by marks. Another student who scores of the maximum marks, gets marks more than the passing marks. The percentage required for passing is :
Q8mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
The pie charts show the market share of companies in the rice market in 2017 and 2018. The value of sales of Company A in 2017 was ₹ 40 lakhs. If its sales grew by 25% in 2018, what was approximate value of sales of company B in 2018?
(Note: Based on standard examination distributions for this question template, Company A's market share was 40% in 2017 and 50% in 2018, while Company B's market share in 2018 was 13.96%.)

image
Q9mediummcqQuantitative AptitudeCompetitive Exam Practice Paper2026
0% accuracy
As a result of hike in the price of rice per kg, a person is unable to purchase more rice for . What was the original price of rice per kg?
Q10mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
A discount of 20% in the price of rice enables X to buy 5kg more rice for ₹ 100. What is the reduced price of rice per kg?
Q11mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
The strength of a school increases and decreases every alternate year by 20%. It started with an increase in 2018. What is the strength of the school at the start of 2021 as compared to that of 2017?
Q12mediummcqQuantitative AptitudeCompetitive Exam 20262026
50% accuracy
The marks (out of 150) of five students in different subjects are given in the following table.
Subject/Student Hindi English Physics Chemistry Mathematics
Ravi 135 140 132 121 141
Deepak 120 135 139 112 136
Sarita 110 126 120 97 130
Kamal 130 125 98 102 120
Divya 136 130 101 100 115
The percentage of marks scored by Ravi in Mathematics is:
Q13mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
Two students appeared for an examination. One student who scored 20 marks more than the other, his score was 60% of the sum of their marks. What was his score?
Q14mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Nazeer spends 20% of his monthly income on housing, 25% of the remaining on education, and saves 10% of the remaining. If his monthly salary is ₹52,600, how much money does he save every month?
Q15mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
The ratio of the number of boys and girls in a college is 6:7. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
Q16mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
The cost price of 27 articles is same as the selling price of 18 articles. What is the profit percent?
Q17mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
A person spends 40% of his salary on food items, 50% of the remaining on transport, and 30% of the remaining on clothes. After spending on food, transport and clothes, he saves ₹1,260 every month, what is his monthly salary?
Q18mediummcqQuantitative AptitudeUP Police Constable2026
50% accuracy
The following pie charts represent the distribution of candidates who were enrolled for an exam and the candidates (out of those enrolled) who passed the exam in different institutes:

image

The difference between the total number of candidates who passed from institutes and combined and the total number of candidates enrolled from institutes and combined is:
Q19mediummcqQuantitative AptitudeCompetitive Exam2026
50% accuracy
If the cost price of tables is equal to the selling price of tables, then what is the loss percentage?
Q20mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
An article was sold for ₹ 4,000. Had a discount of 10% was being offered, the profit would have been 20%. The cost price of the article was:
Q21mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
Vinod and Sanjay were fighting against each other for the post of a village Pradhan. Sanjay got 47.5% votes and lost the election by 270votes. How many votes did Vinod get (assuming that all the villagers participated in the voting)?
Q22mediummcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
A shopkeeper divided a sum of ₹ between his three sons in a proportion of , and respectively. How much did each son inherit?
Q23mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
A person spends of his income. His income increased by and he increased his expenditure by . His percent savings will then be increased by:
Q24mediummcqQuantitative AptitudePrepp2026
0% accuracy
of Ranita's weekly income is equal to of Bhaskar's weekly income. If Ranita's weekly income is decreased by while Bhaskar's weekly income remains unchanged, the ratio of the weekly incomes of Ranita and Bhaskar becomes respectively. What is the weekly income of Bhaskar (in )?
Q25mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
The ratio of the cost price of an article to its selling price is 432:612. The profit percentage (rounded off to 2 decimal places) on it is:
Q26mediummcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
By selling a table for ₹, a trader gains . Find the cost price of the table.
Q27mediummcqQuantitative AptitudeSSC CPO 20242026
0% accuracy
In an election, of the voters on the voters' list did not cast their votes, while voters cast blank ballots. There were only two candidates, Ramagya and Shravan. The winner, Ramagya, received the support of of all the voters on the list. He received votes more than his rival, Shravan. Find the total number of voters on the list.
Q28mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
45% of Samita's monthly income is equal to 63% of Anil's monthly income. If Samita's monthly income is ₹84,000, what is Anil's monthly income (in ₹)?
Q29mediummcqQuantitative AptitudePrepp2026
0% accuracy
image
The percentage distribution of the number of tires of different brands produced by a specific factory in a year is shown in the given pie-chart. The total number of tires sold is 1350.

What is the difference between the average number of Avon and Firestone tires sold together and the average number of Good year and Dunlop tires sold together?
Q30mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
An amusement park gives an offer to its customers that one person will be given free entry with four other people. What is the effective percentage discount given by the amusement park?
Q31mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
An article is marked above the cost price. If a discount of is given on the marked price of the article, then a final profit of is obtained. Now if C.P. of a new article is and profit is desired then what should be the selling price of that new article?
Q32mediummcqQuantitative AptitudeSSC CPO 20242026
0% accuracy
In an election between two candidates, one received of the total valid votes. of the total votes were invalid. If the total number of votes cast was , find the number of valid votes received by the other candidate.
Q33easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
0% accuracy
The difference between 80% and 65% of the same number is 135. What is 49% of the same number?
Q34mediummcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
0% accuracy
Amit saves 20% of his income. If his income increases by 38% and expenditure increases by 60%, then by what per cent does his saving increase/decrease?
Q35mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
The given pie chart displays the number of patients who come to a clinic per week, for treatment under various heads. The total number of patients who come to the clinic is per week. Study the pie chart and answer the question that follows.(Note: Since percentages/degrees values are typically proportional, we can compute directly using their standard standard values for this question where Trauma + Dexa + Blood works = and OPD + X-ray + Physiotherapy = , or equivalent values leading to the exact percentage)The combined number of patients for the treatment of trauma, dexa and blood works is what percentage (rounded off to 1 decimal place) more or less than the combined number of patients for OPD, X-ray and physiotherapy?

image
Q36mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
A student appeared in papers. The maximum marks are the same for each paper. His marks in this paper are in the proportion of . Overall he scored . In how many papers he received less than marks?
Q37mediummcqQuantitative AptitudePrepp2026
0% accuracy
Study the given table and answer the following question. The table shows the number of students studying in 6 different classes of 6 different schools:

image

The number of students studying in class X from school P is approximately what percent of the total number of students studying in class X from all schools together?
Q38mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
S.P. of articles is equal to C.P. of articles. Find the loss or profit percentage.
Q39mediummcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
Kumar lent an amount to Arif at a simple interest rate of p.a. for years, and Arif lent this amount to Naresh at a simple interest rate of p.a. for years. If the interest Arif received was ₹ after years, then what was the amount that Kumar had lent to Arif?
Q40mediummcqQuantitative AptitudeCompetitive Exam2026
Find the value of k in the following.
45% of 880−k% of 450=61.2% of 500
Q41mediummcqQuantitative AptitudePrepp2026
On account of coronavirus, of the population of a village died. Out of the remaining population, fled due to panic. If the present population is , then what was the population of the village before the corona attack?
Q42mediummcqQuantitative AptitudePrepp2026
Study the given table and answer the question that follows.
The table shows the percentage population of four states below poverty line and the proportion of male to female.

image

If the population of states A and D is each, then what is the total number of females below the poverty line in these states combined?
Q43mediummcqQuantitative AptitudeSSC GD Constable2026
A man donates 5% of his monthly income to an orphanage and deposits 20% of the remaining income in a bank. If he is left with Rs. 14,250, find his monthly income.
Q44mediummcqQuantitative AptitudeCompetitive Exam2026
The population of a village increases by 6.25% every year. If the present population of the village is 4046, then what was its population 2 years ago?
Q45mediummcqQuantitative AptitudeSSC GD Constable2026
In an election, a candidate who gets 78% votes is elected by a margin of 504 votes. What is the total number of votes polled?
Q46mediummcqQuantitative AptitudeSSC GD Constable2026
The population of a town 2 years ago was 62,500. Due to migration to cities, it decreases every year at the rate of 4% per annum. Find its present population.
Q47mediummcqQuantitative Aptitude@NUM: 55Competitive Exam2026
There are girls and boys in a music club. new girls join the club. What is the percentage of girls in the club now?
Q48mediummcqQuantitative AptitudePractice Mock2026
The present population of a city is 60,000. If the rate of increase is 10% per year, find the population of the city after 2 years.
Q49mediummcqQuantitative AptitudePractice Mock2026
If 23% of 'x' is 46, then 'x' is ________
Q50hardmcqQuantitative AptitudeCompetitive Exam2026
A manufacturer undertakes to supply pieces of a particular component at per piece. According to his estimates, even if components fail to pass the quality test, then he will make a profit of . However, as it turned out, of the components were rejected. Then what is the loss to the manufacturer?
Q51easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
The cost price of an article is less than its selling price. What is the profit or loss percentage (to the nearest integer)?
Q52mediummcqQuantitative Aptitude@NUM: 61Competitive Exam2026
A man spends ₹ per month from his salary. He saves of his salary. What is his salary (in ₹) for the whole year?
Q53mediummcqQuantitative AptitudePractice Mock2026
In an election, there were three candidates - A, B and C. The winner, A, got five times the votes received by C. B got 240 votes which was 1.5 times the votes of C. How many total votes were polled in the election if there were no bogus votes?
Q54mediummcqQuantitative AptitudeSSC CGL2026
The monthly income of Reena was ₹75,200 and her monthly expenditure was ₹22,500. Next year, her income increased by 25% and her expenditure by 14%. Find the percentage increase in her savings (rounded off to 2 decimal places).
Q55mediummcqQuantitative Aptitude@NUM: 67Competitive Exam2026
A store announces a discount of and then allows another discount of . What is the final sale price (in ₹, to the nearest integer) of a bed whose marked price is ₹?
Q56easymcqQuantitative AptitudeSSC CGL2026
A single discount equivalent to three successive discounts of 10%, 12% and 15% is:
Q57easymcqQuantitative AptitudeSSC CGL2026
If 70 is subtracted from 70% of a number, the remainder is 70. What is the number?
Q58easymcqQuantitative AptitudeSSC CGL2026
The following table shows the percentage of marks obtained by five students in four subjects in an examination.
Student/Subject Maths Physics Chemistry Computer Science
A 90% 65% 76% 64%
B 67% 93% 55% 56%
C 85% 61% 70% 80%
D 59% 75% 84% 91%
E 94% 48% 99% 99%
How many students scored more than 60% of marks in all the four subjects?
Q59mediummcqQuantitative AptitudeCompetitive Exam2026
If a equals 20% of c and b equals 40% of c, then which one of the following is 150% of b?
Q60mediummcqQuantitative AptitudeCompetitive Exam2026
Two numbers A and B are respectively 80% and 50% more than the third number C. What is the ratio of A and B?
Q61mediummcqQuantitative AptitudeCompetitive Exams2026
Study the given pie-chart data and answer the question that follows.

image

If ₹ was spent on Football, then the money spent on Tennis and Basketball taken together is what percentage (rounded off to decimal places) of money spent on Hockey and Cricket taken together?
Q62mediummcqQuantitative AptitudeCompetitive Exam2026
If of a number is , then find of that number.
Q63mediummcqQuantitative AptitudeCompetitive Exam Paper2026
If the sales tax be reduced from to , what difference does it make to a person who purchases an article whose marked price is ?
Q64mediummcqQuantitative AptitudeCompetitive Exam2026
If each side of a square field is increased by , then by what percentage has the area of the field increased?
Q65mediummcqQuantitative AptitudeCompetitive Exam2026
A number is decreased by and then increased by . What is the net increase or decrease per cent in the number?
Q66mediummcqQuantitative AptitudePrepp2026
In a class, the numbers of boys and girls are in the ratio of . What is the percentage of boys in the class?
Q67mediummcqQuantitative AptitudeCompetitive Exam2026
The price of notebooks increased by 15%. How many notebooks can be purchased for the amount of money that was sufficient to purchase 253 notebooks?
Q68hardmcqQuantitative AptitudeCompetitive Exam2026
image
The provided pie-chart shows the percentage distribution of the expenditure incurred in publishing a book. Study the pie-chart and answer the question based on it.

If the marked price of a book is set at above the cost price, and the marked price is , what is the cost of the paper used in one copy of the book?
Q69mediummcqQuantitative AptitudeSSC GD Constable2026
Krishna bought a computer and paid 25% less than its original price. He sold it at 48% profit on the price he had paid. Find the percentage of profit earned by Krishna on the original price.
Q70mediummcqQuantitative AptitudeCompetitive Exam2026
If two numbers are in the ratio
5
4

:
6
5

, then by what percentage is the first number more or less than the second number?
Q71mediummcqQuantitative AptitudeSSC GD Constable2026
The initial population of a country is 2,04,800. If the birth and the death rates are 12% and 7%, respectively, then find the population of the country after 2 years.
Q72easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
Two years ago, a survey revealed that 2400 students in a college were able to use computers at home. This year, the number of students who are able to use computers at home has increased by 30%. How many students are now able to use computers at home?
Q73mediummcqQuantitative AptitudePractice Mock2026
On selling 2800 school bags, Anita earns a profit equal to the sale price of 420 school bags. What is the gain percentage that Anita earned?
Note: round off to two decimal places
Q74mediummcqQuantitative Aptitude@NUM: 57Competitive Exam2026
A shopkeeper bought dozen eggs at ₹ per egg. eggs broke in transportation. He sold the remaining eggs at ₹ each. What is his profit or loss per cent?
Q75mediummcqQuantitative AptitudePractice Mock2026
Ram buys 13 balls for Rs. 390 and sells them at the rate of Rs. 33 per ball. Find his gain percentage.
Q76mediummcqQuantitative AptitudeAdda2472026
A factory's yearly budget for the purchase of employees' protection shoes increased by this year over last year. If the price of the shoes increased by this year, then the number of shoes it can purchase this year is what percent greater than the number of shoes it purchased last year?
Q77mediummcqQuantitative AptitudePractice Mock2026
If the selling price of 10 chairs is the same as the cost price of 8 chairs, find the loss percentage.
Q78mediummcqQuantitative Aptitude@NUM: 62Competitive Exam2026
The savings of a man is equal to of his expenditure. If his income increases by and expenditure increases by , then his savings will increase by:
Q79mediummcqQuantitative AptitudeSSC CGL2026
The given pie-chart shows the number of students admitted into various schools, A, B, C, D, E, in a town. The total number of students is 6500. The number of boys in each school is given by the table. Study the pie-chart and the table carefully and answer the question that follows.
Note: For the purpose of calculation, the degree distributions for schools A, B, C, D, and E in the pie chart correspond to total strength proportions that yield total students as follows: A = 1400, B = 1500, C = 1000, D = 1100, E = 1500 (Total = 6500).

Schools A B C D E
Number of boys 800 850 600 700 765
The total number of boys in schools A, C, D is what percentage of the total number of girls in schools B, C, E (rounded to 2 decimal places)?

image
Q80mediummcqQuantitative AptitudeCompetitive Exam2026
If of a number is , what is the value of the number after increasing it by ?
Q81mediummcqQuantitative AptitudeCompetitive Exam2026
In an election, the total number of valid votes cast was 3,75,000. Candidate A secured 48% of the valid votes, with the rest of the valid votes going to the winner, Candidate B. By how many valid votes did Candidate B win over Candidate A?
Q82mediummcqQuantitative AptitudeCompetitive Exam2026
The valuation of a house depreciates at 10% in a year, compared to its value at the beginning of that year. If the current value of the house is Rs. 40,00,000, find what the value of the house will be three years from now.
Q83mediummcqQuantitative AptitudeCompetitive Exam2026
In an election, two candidates contested. The winner secured 54% of the votes and won by 256 votes. Find the total number of votes polled if 96 votes were declared invalid?
Q84easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
A number is first decreased by and then increased by . What is the net increase or decrease percentage?
Q85easymcqQuantitative AptitudeCompetitive Exam2026
Shweta spends 21% of her monthly salary on house rent, 14% on education, and 13% on entertainment, and still saves ₹5,408. What is her monthly salary (in ₹)?
Q86mediummcqQuantitative AptitudeCompetitive Exam2026
During 2021, the population of a city increased by 8% and in 2022, it increased by 10%. At the end of 2022, its population was 47520. The population of the city at the end of 2021 was:
Q87easymcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
of which of the following numbers is ?
Q88mediummcqQuantitative AptitudeCompetitive Exam2026
Which of the following schemes will yield minimum discount?
2 successive discounts of 5% and 5%

Single discount of 10%

2 successive discounts of 8% and 2%
Q89easymcqQuantitative AptitudeAdda2472026
The ratio of cost price and selling price is , then the loss percent is:
Q90mediummcqQuantitative AptitudeCompetitive Exam2026
In a school, an exam was held for 80 marks in which 32 was the passing marks. Who among the following scored the minimum marks?
[Note: Round off up to one decimal only.]
Q91mediummcqNumerical AbilityUP Police Constable2026
In an entrance test one requires 522 marks out of a maximum of 600 to qualify. What is the cut-off in percentage terms?
Q92mediummcqQuantitative AptitudeCompetitive Exam2026
In a company, 35% of employees are from a science background and
5
1


th
are from an arts background. The rest are either illiterate or with a commerce background. The number of illiterate is 300 which is
2
1

of the commerce background. How many employees are from science or arts background?
Q93mediummcqQuantitative AptitudeCompetitive Exam2026
A man saves ₹6,000 per month from his salary. He spends of his salary each month. What is his annual salary (in ₹)?
Q94mediummcqQuantitative AptitudeCompetitive Exam2026
If is of , then what percent of is ?
Q95mediummcqQuantitative AptitudeCompetitive Exam2026
Sandeep spends 32% of his annual income on food, 20% of the remaining income on travelling, and 35% of the remaining income on clothes, and still saves ₹70,720 per year. What is the annual income (in ₹) of Sandeep?
Q96mediummcqQuantitative AptitudeCompetitive Exam2026
The increase in the price of a certain item was . Then the price was decreased by and then again increased by . What is the resultant increase in the price?
Q97mediummcqQuantitative AptitudeCompetitive Exam Paper2026
A reduction of in the price of rice enables a customer to purchase more for . What is the original price of rice per kg?
Q98mediummcqGeneral Intelligence and ReasoningCompetitive Exam2026
A school has four sections A, B, C, D of Class IX students.

image

Which section exhibits the highest pass percentage in either of the two examinations?
Q99mediummcqQuantitative AptitudeStaff Selection Commission2026
A person, while trading the shares of a particular company, observes that its price has gone down by 10% from the previous day. In anticipation of increment on the next day, he holds it for the next day. But the share price further falls down by another 8% of the previous day. Then he sells his shares and gets ₹12,420. How much could he have saved had he sold it the previous day?
Q100mediummcqQuantitative AptitudeStaff Selection Commission2026
The price of an AC increases and decreases in every alternate year by 13
3
1

%. It started with an increase in 2004. The price of the AC in 2007, as compared to that in 2004 (correct to two places of decimals):

Frequently Asked Questions

How many Percentage questions are on ExamTest.live?
We have 115 Percentage questions spread across 2 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are Percentage MCQs free?
Yes. All Percentage questions, answers, and explanations on ExamTest.live are completely free. No account or subscription required.
Which exams include Percentage questions?
Percentage questions are commonly asked in Quantitative Aptitude, Quantitative Aptitude@NUM: 57, General Intelligence and Reasoning, Numerical Ability, Quantitative Aptitude@NUM: 55. You can filter by exam using the links above.
How do I practice Percentage questions effectively?
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.