UPSC question paper – 1995 – 2000-Arithmetic




#1. In a class there are 18 boys who are over 160 cm tall. If these boys constitute three fourths of the boys and the total number of boys is two-third of the number of students in the class, then what is the number of girls in the class? [2000]

#2. The given diagram shows the number of students who failed in an examination comprising papers in English, Hindi and Mathematics. The total number of students who took the test is 500. What is the percentage of students who failed in atleast two subject? [2000]

#3. If x = –2, then x3 – x2 – x – 1 is equal to [2000]

#4. The monthly income of Komal and Asha are in the ratio of 4 : 3. Their monthly expenses are in the ratio of 3 : 2. However, both save ` 600 per month. What is their total monthly income? [2000]

#5. An accurate clock shows 8 o' clock in the morning. Throughout how many degrees will the hour hand rotate, when the clock shows 2 o'clock in the afternoon? [2000]

#6. A club has 108 members. Two-thirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in the club? [2000]

#7. In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% took Mathematics. The total number of candidates was 2000. How many candidates took both Physics and Mathematics? [2000]

#8. In a town 25% families own a phone and 15% own a car. 65% families own neither a phone nor a car. 2000 families own both a phone and a car. Consider the following statements in this regard: [1999] 1. 10% families own both a car and a phone 2. 35% families own either a car or a phone 3. 40,000 families live in the town Which of the above statements are correct?

#9. In the sequence of numbers 5, 8, 13, X, 34, 55, 89, . . ., the value of X is [1999]

#10. Amar, Akbar and Anthony are friends, being looked after by a matron Farah, Amar weighs 50% more than Akbar and Anthony weighs 25% less than Amar. Farah weighs a third of the combined weight of the three boys. All four together weigh 232kg. The correct arrangement of the persons in the ascending order of their weights, is : [1999]

#11. In an office, the distribution of work hours is as shown in the following table [1999] Consider the following inferences drawn from the table: 1. The average number of hours worked by a staff member is about 30 2. The percentage of those who worked 3.5 or more hours is less than 25 3. At least 5 staff members worked more than 44 hours Which of these inferences is/are valid?

#12. If x + 2y = 2x + y, then x 2 /y 2 is equal to [1999]

#13. The missing fraction in the series given below is: [1998]

#14. In a family, a couple has a son and daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. What is the age of the mother? [1998]

#15. Out of the three annual examination, each with a total of 500 marks, a student secured average marks of 45% and 55% in the first and second annual examinations. To have an overall average of 60%, how many marks does the student need to secure in the third annual examination? [1998]

#16. If 15 pumps of equal capacity can fill a tank in 7 days, then how many extra pumps will be required to fill the tank in 5 days? [1998]

#17. A man purchases two clocks A and B at a total cost of ` 650. He sells A with 20% profit and B at a loss of 25% and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively? [1998]

#18. An accurate clock shows the time as 3.00. After hour hand has moved 135°, the time would be [1998]

#19. There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. 10 students can speak both English and Hindi. If the number of students who can speak English is 21, then how many can speak Hindi, how many can speak only Hindi and how many can speak only English? [1998]

#20. The number of times in a day the Hour-hand and the Minute- hand of a clock are at right angles, is [1997]

#21. A survey was conducted on a samples of 1000 persons with reference to their knowledge of English, French and German. The results of the survey are presented in the given Venn diagram. The ratio of the number of the persons who do not know any of the three languages to those who know all the three language, is [1997]

#22. In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujrati. In that group none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group? [1997]

#23. The average monthly income of person in a certain family of 5 Persons is `1000. What will be monthly average income of person in the same family if the income of one person increased by Rs 12000 per year? [1997]

#24. If A = x² – y², B = 20 and x + y = 10, then [1996]

#25. If the price of a television set is increased by 25%, then by what percentage should the new price be reduced to bring the price back to the original level? [1996]

#26. A person earns ` 2000 per month over and above his salary as additional charge allowance. However, 30% of this additional income will be deducted as additional income tax at source. If the person would deposit ` 1000 per month on a long term saving fetching 12% interest his tax liability on the additional allowance would reduce to 10%. What is the effective interest for this person for money invested in the long term savings scheme? [1995]

#27. Out of a total of 120 musicians in a club, 5% can play all the three instruments, guitar, violin and flute. If so happens that the number of musicians who can play any two or only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone? [1995]

#28. In track meets both 100 yards and 100 metres are used as distances; By how many metres is 100 metres longer than 100 yards? [1995]


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