UPSC IAS Prelims Base – Arithmetic

In track meets both 100 yards and 100 metres are used as distances; By how many metres is 100 metres longer than 100 yards?

The value of (a – m) (b – m)….. (y – m) (z- m) is

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 and 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?

Zero was invented by

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?

The average of x₁ ,x₂ and x₃ is 14.Twice the sum of x₂ and x₃ is 30. What is the value of x₁?

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?

If A=x² – y²,B= 20 and x+y=10,then

The average monthly income of person in a certain family of 5 is ₹ 1000. What will be monthly average income of person in the same family if the income of one person increased by ₹ 12000 per year?

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

The number of times in a day the Hour-hand and the Minute-hand of a clock are at right angles, is

The number of times in a day the Hour-hand and the Minute-hand of a clock are at right angles, is 

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?

An accurate clock shows the time as 3.00. After hour hand has moved 135°, the time would be

A man purchases two clocks A and 8 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?

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?

Out of the three annual examination, each with a total of 5(X) 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?

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?

The missing fraction in the series given below is :

4/9, 9/20, …., 39/86

If x +2y = 2x + y, then x² /y² is equal to

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 232 kg. The correct arrangement of the persons in the ascending order of their weights, is :

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 232 kg. The correct arrangement of the persons in the ascending order of their weights, is :

In the sequence of numbers 5, 8, 13, X ,34, 55, 89, …, the value of X is

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:

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?

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?

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?

An accurate clock shows 8 0′ clock in the morning. Throughout how many degrees will the hour hand rotate, when the clock shows 2 0′ clock in the  afternoon?

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?

If x = -2, then x³ – x² – x -1 is equal to

If x = -2, then x³ – x² – x -1 is equal to

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?

For the system of equations x²+ y² = 34,  x⁴ -y⁴ = 544, the values of x and y are

Water is filled in a container in such a manner that its volume doubles after every five minutes. If it takes 30 minutes for the container to be full, in how much time will it be one-fourth full?

A city has a population of 3,00,000 out of which 1,80,000 are males. 50% of the population is literate. If 70% of the males are literate, the number of literate females is

In a survey, it was found that 80% of those surveyed owned a car while 60% of those surveyed owned a mobile phone. If 55% owned both a car and a mobile phone, what percent of those surveyed owned a car or a mobile phone or both?

In 1930, a person’s age was 8 times that of his shown. In 1938, the father’s age became ten times that of his son’s age in 1930. The ages of the son and father in 1940 were respectively

Amit started a business by investing ₹ 30,000. Rahul joined the business after some time and invested ₹ 20,000. At the end of the year, profit was divided in the ratio of 2 : 1. After how many months did Rahul join the business?

When the time in the wall-clock is 3.25 p.m., the acute angle between the hours-hand and the minutes-hand  is

The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double of the sum of the ages of his sons. The father’s present age is

In a company, 60%of the employees are men. Of these 40% are drawing more than 50,000 per year. If 36% of the total employees of the company draw more than ! 50,000 per year, what is the percentage of women who are drawing less than 50,000 per year?

A trader fixed the price of an article in such a way that by giving a rebate of 10% on the price fixed, he made a profit of 15%. If the cost of the article is ₹ 72 the price fixed on it,  is

Three bells toll at intervals of 9, 12 and 15 minutes respectively. All the three begin to toll at 8 a.m. At what time will they toll together again?

Left pan of a faulty weight weighs 100 gram more than its right pan. A shopkeeper keeps the weight measure in the left pan while buying goods but keeps it in the right pan while selling his goods. He uses only 1 kg weight measure. If he sells his goods at the listed cost price, what is his gain?

There are 6 person ; A ,B, C, D, E and F. A has 3 items more than C

D has 4 items less than 8
E has 6 items less than F
C has 2 items more than E
F has 3 items more than D

Which one of the following figure can not be equal to the total number of items possessed by all the 6 persons?

How many numbers are there in all from 6000 to 6999 (Both 6000 and 6999 included) having all digits same?

Each of the five persons A, B, C, D and E possesses unequal number of similar items. A, B and C possesses Twenty-one items in all, while C, D and E possess seven items in all. How many items do A and B possess in all?

Each of the five persons A, B, C, D and E possesses unequal number of similar items. A, B and C possesses Twenty-one items in all, while C, D and E possess seven items in all. How many items do A and B possess in all?

6 equidistant vertical lines are drawn on a board 6 equidistant horizontal lines are also drawn on the board cutting the 6 vertical lines, and the distance between any two consecutive horizontal lines is equal to that between any two consecutive vertical lines. What is the maximum number of squares thus formed?

A person has to completely put each of three liquids 403 litres of petrol, 465 litres of diesel and 496 litres of Mobile Oil in bottles of equal size without mixing any of the above three types of liquids such that each bottle is completely filled. What is the least possible number of bottles required?

If all the numbers from 501 to 700 are written, what is the total number of times does the digit 6 appear?

The average salary of 100 employees in an office is ₹ 16,000 per month. The management decided to raise salary of every employee by 5% but stopped a transport allowance of ₹ 800 per month which was paid earlier to every employee. What will be the new average monthly salary?

In the series

AABABCABCDABCDE..
Which letter occupies the 100th position?

What is the number of terms in the series 117, 120, 123,
126,…….. ….. .,333?

A person purchases 100 pens at a discount of 10%. The net amount of money spent by the person to purchase the pens is ₹ 600. The selling expenses incurred by the person are 15% on the net cost price. What should be the selling price for 100 pens in order to earn a profit of 25%?

In an examination, 70% of the students passed in the Paper I, and 60% of the students passed in the Paper II. 15% of the students failed in both the papers while 270 students passed in both the papers. What is the total number of students?

March 1, 2008 was Saturday. Which day was it on March 1, 2002?

There are four persons A, B, C, D; and A has some coins. A gave half of the coins to B and 4 more besides. B gave half of the coins to C and 4 more besides. C gave half of the coins to D and 4 more besides. Both B and D end up with same number of coins. How many coins did A have originally?

While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed?

Four metal rods of lengths 78 cm, 104 cm 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the 68. maximum number of pieces that can be cut?

In an examination, there are three subjects A, B and C. A student has to pass in each subject. 20% students failed in A, 22% students failed in B and 16% failed in C. The total number of students passing the whole examination lies between

How many times are an hour hand and a minute hand of a clock at right angles during their motion from 1.00 p.m. to 10.00 p.m.?

There are 240 balls and n number of boxes B₁, B₂, B_3, …… B11. The balls are to be placed in the boxes such that B₁ should contain 4 balls more than B₂, B₂ should contain 4 balls more than 8₃, and soon. Which one of the following cannot be the possible value of n?

In a tournament 14 teams play league/matches. If each team plays against every other team only once then how many matches are played?

Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X ?

How many numbers from 0 to 999 are not divisible by either 5 or 7 ?

In a group of five persons A, B, C, D and E, there is a professor, a doctor and lawyer. A and D are unmarried ladies, and do not work. Of the married couple in the Group, E is the husband. B is the brother of A and is neither a doctor nor a lawyer. Who is the professor ?

Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are below twenty five. Then, which one of the following is certainly true?

Each person’s performance compared with all other persons is to be done to rank them subjectively. How many comparisons are needed in total, if there are 11 persons

A man fills a basket will eggs in such a way that the number of eggs added on each successive day is the same as the number already present in the basket. This way the basket gets completely filled in 24 day.After how many days the basket was 4^th full?

The difference between the simple interest received  from two banks on ₹ 500 for two years is ₹ 2.50. What is the difference between their rates?

A candidate attempted 12 questions and secured full marks in all of them. If he obtained 60% in the test and all questions carried equal marks, then what is the number of questions in the test?

A contract on construction job specifies a penalty for delay in completion of the work beyond a certain date is as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day etc., the penalty for each succeeding day being ₹ 50 more than that of the preceding day. How much penalty should the contractor pay if he delays the work by 10 days?

A contract on construction job specifies a penalty for delay in completion of the work beyond a certain date is as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day etc., the penalty for each succeeding day being ₹ 50 more than that of the preceding day. How much penalty should the contractor pay if he delays the work by 10 days?

A person has only ₹ 1 and ₹ 2 coins with her. If the total number of coins that she has is 50 and the amount  of money with her is ₹ 75, then the number of ₹ 1 and ₹ 2 coins are, respectively

Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance incomplete steps?

A student on her first 3 tests received an average score of N points. If she exceeds her previous average score by 20 points on her fourth test, then what is the average score for the first 4 tests?

In a group of persons, 70% of the persons are male and 30% of the persons are married. If two-sevenths of the males are married, what fraction of the females is single ?

In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1 : 2. Based on the information, the total number of coins in the collection now becomes

A gardener has 1000 plants. He wants to plant them in such a way that the number of rows and the number of columns remains the same. What is the minimum number of plants that he needs more for this purpose?

A sum of ₹ 700 has to be used to give seven cash prizes to the students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, what is the least value of the prize?

Out of 120 applications for a post, 70 are male and 80 have a driver’s license. What is the ratio between the minimum to maximum number of males having driver’s license?

In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food?

The tank-full petrol in Arun’s motor-cycle lasts for 10  days. If he starts using 25% more everyday, how many days will the tank-full petrol last?

There are some balls of red, green and yellow colour lying on a table. There are as many red balls as there are yellow balls. There are twice as many yellow balls as there are green ones. The number of red balls.

Fora charity show, the total tickets sold were 420. Half of these tickets were sold at the rate of ₹ 5 each, one-third at the rate of ₹ 3 each and the rest for ₹ 2 each. What was the total amount received?

If Sohan, while selling two goats at the same price, makes a profit of 10% on one goat and suffers a loss of 10% on the other

Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and 12 seconds respectively. The number of times they would fire the bullets together at the target in an hour is

A bell rings every 18 minutes. A second bell rings every 24 minutes. A third bell rings every 32 minutes. If all the three bells ring at the same time at 8 o’clock in the morning, at what other time will they all ring together?

As per agreement with a bank, a businessman had to refund a loan in some equal instalments without interest. After paying 18 instalments he found that 60 percent of his loan was refunded. How many instalments were there in the agreement?

A person X has four notes of Rupee 1, 2, 5 and 10  denomination. The number of different sums of money she can form from them is

There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% students play both the games. What is the number of students who play neither cricket nor football?

Each of A, B, C and D has ₹ 100.A pays ₹ 20 to B, who pays ₹ 10 to C, who gets ₹ 30 from D. In this context, which one of the following statements is not correct?

In a town, 45% population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazinesB and C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine

Two equal glasses of same type are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot?

In a test, a candidate attempted only 8 questions and secured 50% marks in each of the questions. If he obtained a total of 40% in the test and all questions in the test carried equal marks, how many questions were there in the test?

A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father’s and the mother’s age is 51 years. What is the age of the son ?

The monthly incomes of Peter and Paul are in the ratio of 4 : 3. Their expenses are in the ratio of 3 : 2. If each saves ₹ 6,000 at the end of the month, their monthly incomes respectively are (in ₹)

The monthly incomes of Peter and Paul are in the ratio of 4 : 3. Their expenses are in the ratio of 3 : 2. If each saves ₹ 6,000 at the end of the month, their monthly incomes respectively are (in ₹)

A cow costs more than 4 goats but less than 5 goats. If a goat costs between ₹ 600 and ₹ 800, which of the following is a most valid conclusion?

A cow costs more than 4 goats but less than 5 goats. If a goat costs between ₹ 600 and ₹ 800, which of the following is a most valid conclusion?

Candidates in a competitive examination consisted of 60% men and 40% women. 70% men and 75% women cleared the qualifying test and entered the final test where 80% men and 70% women were successful.
Which of the following statements is correct?