eLitmus Question Paper

Number System 01

01. The number of common terms in the two sequences 17, 21, 25, ….. , 417 and 16, 21, 26, …,466 is ?

(a) 19 (b) 20 (c) 77 (d) 22

02. How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed ??

(a) 374 (b) 500 (c) 375 (d) 376

03. What is the number of distinct terms in the expansion of (a + b + c)20 ?

(a) 231 (b) 253 (c) 242 (d) 210

04. What are the last two digits of 72008 ?

(a) 21 (b) 61 (c) 01 (d) 41

05. The integers 1, 2, 3, … 40 are written on blackboard. The following operation is then repeated 39 times. In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b – 1 is written. What will be the number left on the board at the end ?

(a) 820 (b) 821 (c) 781 (d) 819

06. An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …, 9. But on the slip on which the code is hand written allows confusion between top and bottom, because there are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?

(a) 25 (b) 75 (c) 80 (d) None of these

07. A young girl counted in the following way on the fingers of her left hand. She started calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5, then reversed direction, calling the ring finger 6, middle finger 7, index finger 8 and thumb 9 and then back to the index finger for 10, middle finder for 11 and so on. She counted up to 1994. She ended on her ?

(a) thumb (b) index finger (c) middle finger (d) ring finger

08. Let U(n+1)= 2Un + 1, ( n=0, 1, 2, …………) U0=0 then U(10) would be nearest to ?

(a) 1023 (b) 2047 (c) 4095 (d) 8195

09. The product of all integers from 1 to 100 will have the following numbers of zeros at the end ?

(a) 20 (b) 24 (c) 19 (d) 22

10. The number of positive integers not greater than 100, which are not divisible by 2, 3 or 5 is ?

(a) 26 (b) 18 (c) 31 (d) None of these

Answers :

1. B 2. D

3. A 4. C

5. C 6. C

7. B 8. A

9. B 10. A

Number System 02

01. If n is any odd number greater than 1, then n(n2 - 1) is always divisible by ?

(a) 96 (b) 48 (c) 24 (d) None of these

02. If a number 774958A96B is to be divisible by 8 and 9, the respective values of A and B will be

(a) 7 and 8 (b) 8 and 0 (c) 5 and 8 (d) None of these

03. Three consecutive positive even numbers are such that thrice the first number exceeds double the third by 2, the third number is ?

(a) 10 (b) 14 (c) 16 (d) 12

04. Three bells chime at intervals of 18 min, 24 min and 32 min respectively. At a certain time, they begin to together, What length of time will elapse before they chime together again ?

(a) 2 h and 24 min (b) 4h and 48 min (c) 1 h and 36 min (d) 5h

05. Two positive integers differ by 4 and sum of their reciprocals is 10/21. Then, one of the numbers is ?

(a) 3 (b) 1 (c) 5 (d) 21

06. (56-1) is divisible by ?

(a) 13 (b) 31 (c) 5 (d) None of these

07. The remainder obtained when a prime number greater that 6 is divided by 6 is

(a) 1 or 3 (b) 1 or 5 (c) 3 or 5 (d) 4 or 5

08. For the product n(n+1)(2n+1) , which one of the following is not necessarily true ?

(a) It is even (b) Divisible by 3 (c) divisible by (n(n+1)(2n+1))/2 (d) Never divisible by 237

09. 72 Hens Rs …96.7.. Then what does each hen cost, where two digits in place of “…. , …..”are not visible written in illegible hand-writing ?

(a) Rs 3.23 (b) Rs 5.11 (c) Rs 5.51 (d) Rs 7.22

10. Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 16, is 4?

(a) 137 (b) 1361 (c) 140 (d) 172

Answers

1. C 2. B

3. B 4. B

5. A 6. B

7. B 8. D

9. C 10. D

Permutations And Combinations 01

01. Five-digit numbers are formed using only 0, 1, 2, 3, 4 exactly once. What is the difference between the greatest and smallest numbers that can be formed ?

(a) 19800 (b) 41976 (c) 32976 (d) None of these

02. In how many ways can Eight Directors, Vice-Chairman and Chairman of a firm be seated at a round table, if the Chairman has to sit between the Vice-Chairman and a Director ?

(a) 9! x 2 (b) 2 x 8! (c) 2 x 7! (d) None of these

03. A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be 3 exactly girls in the invitees ?

(a) 320 (b) 160 (c) 80 (d) 200

04. Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and they which are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then, how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects ?

(a) 8 (b) 10 (c) 15 (d) 22

05. A, B, C, D are four towns, any three of which are non-collinear. Then, the number of ways to construct three roads each joining a pair of towns so that the roads do not form a triangle is ?

(a) 7 (b) 8 (c) 9 (d) 24

06. If a 4-digit number is formed with digits 1, 2, 3 and 5. What is the probability that the number is divisible by 25, if repetition of digits is not allowed ?

(a) 1/12 (b) 1/4 (c) 1/6 (d) None of these

07. A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers ?

(a) 6666600 (b) 6666660 (c) 6666666 (d) None of these

08. 139 persons have signed for an elimination tournament. All players are to be paired up for the first round, but because 139 is an odd number one player gets a bye, which promotes him to the second round, without actually playing in the first round. The pairing continues on the next round, with a bye to any player left over. If the schedule is planned so that a minimum number of matches is required to determine the champion, the number of matches which must be played is

(a) 136 (b) 137 (c) 138 (d) 139

09. A box contains 6 red balls, 7 green balls and 5 blue balls. Each ball is of different size. The probability that the red ball selected is the smallest

red ball ?

(a) 1/18 (b) 1/3 (c) 1/6 (d) 2/3

10. A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible ?

(a) 3 (b) 4 (c) 5 (d) 6

Answers :

1. C 2. B

3. B 4. D

5. D 6. A

7. A 8. C

9. C 10. D

Permutation And Combinations 02

01. In a chess competition involving some boys and girls of a school, every student had to play exactly one game with the every other student. It was found that in 45 games both the players were girls and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is ?

(a) 200 (b) 216 (c) 235 (d) 256

02. A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done such that no two adjacent stripes have the same colour is ?

(a) 12 x 81 (b) 16 x 192 (c) 20 x 125 (d) 24 x 216

03. An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, …. 9 such that the first digit of the code is non-zero. The code, handwritten on a slip, can however potentially create confusion, when read upside down- for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise ?

(a) 80 (b) 78 (c) 71 (d) 69

04. How many numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million ?

(a) 496 (b) 486 (c) 1084 (d) 728

05. In how many ways is it possible to choose a white square and a black square on a chess-board so that the squares must not lie in the same row or column ?

(a) 56 (b) 896 (c) 60 (d) 768

06. How many four-letter computer passwords can be formed using only the symmetric letters. (no repetition allowed) (Symmetric letters :- A, H, I, M, O, T, U, V, W, X AND Z)

(a) 7920 (b) 330 (c) 14640 (d) 419430

07. How many three-letter computer password can be formed with at least one symmetric letter ? (Symmetric letters: A, H, I, M, O, T, U, V, W, X and Z)

(a) 990 (b) 2730 (c) 12870 (d) 1560000

08. For a scholarship, at the most n candidates out of 2n+1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is ?

(a) 3 (b) 4 (c) 6 (d) 5

09. Ten points are marked on a straight line and 11 points are marked on another straight line. How many triangles can be constructed with vertices from among the above points ?

(a) 495 (b) 550 (c) 1045 (d) 2475

10. How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at unit’s place must be greater than the in the ten’s place ?

(a) 54 (b) 60 (c) 17 (d) 2 x 4!

Answers :

1. A 2. A

3. D 4. D

5. D 6. A

7. C 8. A

9. C 10. B

Percentage 01

01. The length, breadth and height of a room are in the ratio 3 : 2 : 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will be decreased by ?

(a) 13.64% (b) 15% (c) 18.75% (d) 30%

02. A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options-air conditioning, radio and power windows- were already installed. The survey found : 15 had air conditioning, 2 had air conditioning and power windows but no radios, 12 had radio, 6 had air conditioning and radio but no power windows, 11 had power windows, 4 had radio and power windows, 3 had all three options. What is the number of cars that had none of the options?

(a) 4 (b) 3 (c) 1 (d) 2

03. 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?

(a) p = q (b) p < q (c) p > q (d) p = q/2

04. 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 1944.81. What was the original prices of the painting (in Rs)?

(a) 2756.25 (b) 2256.25 (c) 2500 (d) 2000

05. 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 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 ?

(a) 1 (b) 3 (c) 4 (d) 5

06. 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 represent 60% of 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 ?

(a) 300 (b) 250 (c) 400 (d) 500

07. Forty percent 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 Rs 25,000 per year ?

(a) 2/11 (b) 1/4 (c) 1/3 (d) 3/4

08. In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals : I, II and III, 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals?

(a) 10 (b) 12 (c) 17 (d) 22

09. One bacteria splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produce next generation. If the seventh generation number is 4096 million, what is the number in the first generation?

(a) 1 million (b) 2 million (c) 4 million (d) 8 million

10. I bought 5 pens, 7 pencils and 4 erasers. Rahul bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What percent of the total amount paid by me was paid for the pens ?

(a) 37.5% (b) 62.5% (c) 50% (d) None of these

Answers :

1. D 2. D

3. C 4. A

5. C 6. A

7. D 8. C

9. A 10. B

Percentage 02

01. Ram sells his goods 25% cheaper than Shyam and 25% dearer than Rahul. How much percentage is Rahul’s goods cheaper than Shyam’s ?

(a) 33.33% (b) 50% (c) 66.66% (d) 40%

02. In an election between 2 candidates, Bhiku gets 65% of the total valid votes. If the total votes were 6000, what is the number of valid votes that the other candidate Mhatre gets if 25% of the total votes were declared invalid ?

(a) 1625 (b) 1575 (c) 1675 (d) 1525

03. In an examination, Mohit obtained 20% more than Sushil but 10% less than Rajesh. If the marks obtained by Sushil is 1080, find the percentage marks obtained by Rajesh if the full marks is 2000.

(a) 86.66% (b) 72% (c) 78.33% (d) 77.77%

04. The population of the village of Gavas is 10,000 at this moment. It increases by 10% in the first year. However, in the second year, due to migration, the population drops by 5%. Find the population at the end of the third year if in the third year the population increases by 20%.

(a) 12,340 (b) 12,540 (c) 1,27,540 (d) 12,340

05. In a class, 25% of the students were absent for an exam. 30% failed by 20 marks and 10% just passed because of grace marks of 5. Find the average score of the class if the remaining students scored an average of 60 marks and the pass marks are 33 (counting the final score of the students).

(a) 37.26 (b) 37.6 (c) 37.8 (d) 36.93

06. Ram spends 20% of his monthly income on his household expenditure, 15% of the rest on books, 30% of the rest on clothes and saves the rest. On counting, he comes to know that he has finally saved Rs 9520. Find the monthly income ?

07. Hans and Bhaskar have salaries that jointly amount to Rs 10,000 per month. They spend the same amount monthly and then it is found that the ratio of their savings is 6:1. Which of the following can be Hans’s salary ?

(a) Rs 6000 (b) Rs 5000 (c) Rs 4000 (d) Rs 3000

08. 4/5th of the voters in Bellary promised to vote for Sonia and the rest promised to vote for Sushma. Of these voters, 10% of the voters who had promised to vote for Sonia, did not vote on the election day, while 20% of the voters who had promised to vote for Sushma did not vote on the election day. What is the total no. of votes polled if Sonia got 216 votes ?

(a) 200 (b) 300 (c) 264 (d) 100

09. In an examination, 80% students passed in Physics, 70% in Chemistry while 15% failed in both the subjects. If 325 students passed in both the subjects. Find the total number of students who appeared in the examination ?

(a) 500 (b) 400 (c) 300 (d) 600

10. Ravana spends 30% of his salary on house rent, 30% of the rest he spends on his children’s education and 24% of the total salary he spends on clothes. After his expenditure, he is left with Rs 2500. What is Ravana’s salary ?

(a) Rs 11,494.25 (b) Rs 20,000 (c) Rs 10,000 (d) Rs 15,000

Answers :

1. D 2. B

3. B 4. B

5. B 6. C

7. A 8. C

9. A 10. C

Percentage 03

01. A man earns x% on the first Rs 2,000 and y% on the rest of his income. If he earns Rs 700 from Rs 4,000 and Rs 900 from Rs 5,000 of income, find x%.

(a) 20% (b) 15% (c) 25% (d) None of these

02. The price of a Maruti Car rises by 30% while the sales of the car comes down by 20%. What is the percentage change in the total revenue ?

(a) -4% (b) -2% (c) +4% (d) +2%

03. A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance, he purchases oranges. Number of oranges he can purchase?

(a) 36 (b) 40 (c) 15 (d) 20

04. 2/5 of the voters promise to vote for P and rest promised to vote for Q. Of these, on the last day 15% of the voters went back of their promise to vote for P and 25% of voters went back of their promise to vote for Q, and P lost by 2 votes. Then, the total number of voters is ?

(a) 100 (b) 110 (c) 90 (d) 95

05. The number of votes not cast for the Praja Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls and the Praja Party lost by a majority twice as large as that by which it had won the Assembly polls. If a total 2,60,000 people voted each time, how many voted for the Praja Party in the previous Assembly Polls ?

(a) 1,10,000 (b) 1,50,000 (c) 1,40,000 (d) 1,20,000

06. The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994 is Rs 20 per kg. The inflation rates of the years 1994 and 1995 are expected to be 8% each. the expected price of sugar price on January 1, 1996 would be ?

(a) Rs 23.60 (b) Rs 24.00 (c) Rs 24.20 (d) Rs 24.60

07. A report consists of 20 sheets each of 55 lines and each such line consists of 65 characters. This report is reduced onto sheets each of 65 lines such that each line consists off 70 characters. The percentage reduction in number of sheets is closet to

(a) 20% (b) 5% (c) 30% (d) 35%

08. To pass an examination, 40% marks are essential. A obtains 10% less than the pass marks and B obtains 11.11% marks less than A. What percent less that the sum of A’s and B’s marks should C obtain to pass the exam ?

(a) 40% (b) 41(3/17)% (c) 28% (d) Any of these

09. The hourly wages of a female labour are increased by 12.5%, whereas the weekly working hours are reduced by 8%. Find the percentage change in the weekly wages if she was getting Rs 1200 per week for 50 hours previously.

(a) +3.5% (b) 4% (c) 4.5% (d) None of these

10. Two numbers X and Y are 20% and 28% less than a third number Z. Find by what percentage is the number Y less than the number X.

(a) 8% (b) 12% (c) 10% (d) 9%

Answers

1. B 2. C

3. D 4. A

5. C 6. C

7. A 8. D

9. A 10. C

Percentage 03

01. A man earns x% on the first Rs 2,000 and y% on the rest of his income. If he earns Rs 700 from Rs 4,000 and Rs 900 from Rs 5,000 of income, find x%.

(a) 20% (b) 15% (c) 25% (d) None of these

02. The price of a Maruti Car rises by 30% while the sales of the car comes down by 20%. What is the percentage change in the total revenue ?

(a) -4% (b) -2% (c) +4% (d) +2%

(a) 36 (b) 40 (c) 15 (d) 20

(a) 100 (b) 110 (c) 90 (d) 95

(a) 1,10,000 (b) 1,50,000 (c) 1,40,000 (d) 1,20,000

(a) Rs 23.60 (b) Rs 24.00 (c) Rs 24.20 (d) Rs 24.60

(a) 20% (b) 5% (c) 30% (d) 35%

(a) 40% (b) 41(3/17)% (c) 28% (d) Any of these

(a) +3.5% (b) 4% (c) 4.5% (d) None of these

10. Two numbers X and Y are 20% and 28% less than a third number Z. Find by what percentage is the number Y less than the number X.

(a) 8% (b) 12% (c) 10% (d) 9%

Answers

1. B 2. C

3. D 4. A

5. C 6. C

7. A 8. D

9. A 10. C

Profit & Loss And Ratio & Proportion 01

01. A milkman mixes 20L of water with 80L of milk. After selling one-fourth of this mixture, he adds a water to replenish the quantity that he has sold. What is the current proportion of water to milk ?

(a) 2 : 3 (b) 1 : 2 (c) 1 : 3 (d) 3 : 4

02. Using only 2, 5, 10, 25 and 50 paise coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs 1.01 to three different persons?

(a) 19 (b) 20 (c) 17 (d) 18

03. Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then, the ratio of the shorter side to the longer side is ?

(a) 1:2 (b) 2:3 (c) 1:4 (d) 3:4

04. Mayank, Mirza, Little and Jaspal bought a motorbike for $60,000. Mayank paid one half of the sum of the amounts paid by the other boys, Mirza paid one third of the sum of the amounts paid by the other boys; and Little paid one fourth of the sum of the amounts paid by the other boys. How much did Jaspal has to pay ?

(a) $15,000 (b) $13,000 (c) $17,000 (d) None of these

05. A piece of string is 40 cm long. It is cut into three pieces. The longest piece is 3 times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece(in cm) ?

(a) 27 (b) 5 (c) 4 (d) 9

06. Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20 kg of fresh grapes ?

(a) 2 Kg (b) 2.4 Kg (c) 2.5 Kg (d) None of these

07. I have one rupees coins, fifty paise coins and twenty five paise coins. The number of coins are in the ratio 2.5 : 3 : 4. If total amount with me is Rs 210, find the number of one rupee coins ?

(a) 90 (b) 85 (c) 100 (d) 105

08. After allowing a discount of 11.11% , a trader still makes a gain of 14.28%. At how many percent above the cost price does he mark on his goods ?

(a) 28.56% (b) 35% (c) 22.22% (d) None of these

09. A dealer buys dry fruits at Rs 100, Rs 80 and Rs 60 per kilogram. He mixes them in the ratio 3 : 4 : 5 by weight and sells at a profit of 50%. At what price per kilogram does he sell the dry fruit ?

(a) Rs 80 (b) Rs 100 (c) Rs 95 (d) None of these

10. Two liquids A and B are in the ratio 5 : 1 in container 1 and 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio of 1 : 1 ?

(a) 2 : 3 (b) 4 : 3 (c) 3 : 2 (d) 3 : 4

Answers

1. A 2. A

3. D 4. B

5. C 6. C

7. D 8. A

9. D 10. D

Profit & Loss And Ratio & Proportion 02

01. Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?

(a) 20% (b) 25% (c) 40% (d) 15%

02. I sold two watches for Rs 300 each, one at the loss of 10% and the other at the profit of 10%.What is the percentage of loss(-) or profit(+) that resulted from transaction?

(a) (+)10 (b) (-)1 (c) (+))1 (d) (-)10

03. The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ration 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs 70,000 less. Find the original price of the diamond?

(a) Rs 1.4 lakh (b) Rs. 2 lakh (c) Rs 1 lakh (d) Rs 2.1 lakh

04. A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particular sticky bargainer. How much percent above the cost price were his wares listed?

(a) 100% (b) 80% (c) 75% (d) 66.66%

05. A man buys spirit at Rs 60 per litre, adds water to it and then sells at Rs 75 per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%?

(a) 9 : 1 (b) 10 : 1 (c) 11 : 1 (d) None of these

06. Two oranges, three bananas and four apples cost Rs 15. Three oranges, two bananas and one apple cost Rs 10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?

(a) Rs 10 (b) Rs 8 (c) Rs 15 (d) Cannot be det..

07. From each of two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as large as the smaller. What is the ratio of the two numbers ?

(a) 2:1 (b) 3:1 (c) 3:2 (d) None of these

08. The marked price of a table is Rs. 1200, which is 20% above the cost price. It is sold at a discount of 10% on the marked price. Find the profit percent.

(a) 10% (b) 8% (c) 7.5% (d) 6%

09. If the work done by (x-1) men in (x+1) days is to the work done by (x+2) men in (x-1)days is in the ratio 9:10, then the value of x is ?

(a) 10 (b) 12 (c) 8 (d) 15

10. A cask contains a mixture of 49 litres of wine and water in the proportion 5:2. How much water must be added to it so that the ratio of wine to water may be 7:4 ?

(a) 3.5 (b) 6 (c) 7 (d) None of these

Answers

1. A 2. B

3. C 4. A

5. B 6. C

7. A 8. B

9. C 10. B

Alligations Set 01

01. A mixture of 125 gallons of wine and water contains 20% water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture ?

(a) 10 gals (b) 8.5 gals (c) 8 gals (d) 8.33 gals

02. 4oo students took a mock exam in Delhi, 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination?

(a) 100 (b) 120 (c) 150 (d) 300

03. What will be the ratio of petrol and kerosene in the final solution formed by mixing petrol and kerosene that are present in three vessels of equal capacity in ratios 4 : 1, 5 : 2 and 6 : 1 respectively ?

(a) 166 : 22 (b) 83 : 22 (c) 83 : 44 (d) None of these

04. A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available ?

(a) 20% (b) 25% (c) 33.33% (d) 40%

05. In a Singapore zoo, there are deers and there are ducks. If the heads are counted, there are 180, while the legs are 448. What will be the number of deers in the zoo

(a) 136 (b) 68 (c) 44 (d) 22

06. Two vessels contain a mixture of spirit and water. In the first vessel and ratio of spirit to water is 8 : 3 and in the second vessel the ratio is 5 : 1. A 35 litre cask is filled from these vessels so as to contain a mixture of spirit and water in the ratio of 4 : 1. How many litre are taken from the first vessel ?

(a) 11 litres (b) 22 litres (c) 16.5 litres (d) 17.5 litres

07. In what ratio should water be mixed with soda costing Rs 12 per litre so as to make a profit of 25% by selling the diluted liquid at Rs 13.75 per litre ?

(a) 10:1 (b) 11:1 (c) 1:11 (d) 12:1

08. A 20 percent gain is made by selling the mixture of two types of ghee at Rs 480 per kg. If the type costing 610 per kg was mixed with 126 kg of the other, how many kilograms of the former was mixed ?

(a) 138 kg (b) 34.5 kg (c) 69 kg (d) Cannot be det..

09. A bartender stole champagne from a bottle that contained 50% of spirit and he replaced what he had stolen with champagne having 20% spirit. The bottle then contained only 25% spirit. How much of the bottle did he steal ?

(a) 80% (b) 83.33% (c) 85.71% (d) 88.88%

10. A mixture of 20 litres of brandy and water contains 10% water. How much water should be added to it to increase the percentage of water to 25%?

(a) 2 litres (b) 3 litres (c) 2.5 litres (d) 4 litres

Answers :

1. D 2. A

3. B 4. A

5. C 6. A

7. C 8. D

9. B 10. D

Alligations

Set 02

01. Two containers of equal capacity are full of a mixture of oil and water. In the first, the ratio of oil to water is 4 : 7 and in the second it is 7 : 11. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of oil to water ?

(a) 149 : 247 (b) 247 : 149 (c) 143 : 241 (d) 241 : 143

02. Two vessels contain spirit and water mixed respectively in the ratio of 1 : 3 and 3 : 5. Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 1 : 2 ?

(a) 2 : 1 (b) 3 : 1 (c) 1 : 2 (d) 1 : 3

03. The price of a pen and pencil is Rs 35. The pen was sold at a 20% profit and the pencil at a 10% loss. If in the transaction a man gains Rs 4, how much is cost price of the pen ?

(a) Rs 10 (b) Rs 25 (c) Rs 20 (d) None of these

04. A person purchased a cupboard and a cot for Rs 18,000. He sold the cupboard at a profit of 20% and the cot at a profit of 30%. If his total profit was 25.83%, find the cost price of the cupboard ?

(a) Rs 10,500 (b) Rs 12,000 (c) Rs 7500 (d) Rs 10,000

05. A vessel is full of a mixture of kerosene and petrol in which there is 18% kerosene. Eight litre are drawn off and then the vessel is filled with petrol. If the kerosene is now 15%, how much does the vessel hold ?

(a) 40 litres (b) 32 litres (c) 36 litres (d) 48 litres

06. Two solutions of 90% and 97% purity are mixed resulting in 21 litres of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture ?

(a) 15 litres (b) 12 litres (c) 9 litres (d) 6 litres

07. In what ratio should water be mixed with soda costing Rs 12 per litre so as to make a profit of 25% by selling the diluted liquid at Rs 13.75 per litre ?

(a) 10 : 1 (b) 11 : 1 (c) 1 : 11 (d) 12 : 1

08. A sum of Rs 36.90 is made up of 90 coins that are either 20 paise coins or 50 paise coins. Find out how many 20 paise coins are there in the total amount ?

(a) 47 (b) 43 (c) 27 (d) 63

09. A bonus of Rs 9,85,000 was divided among 300 workers of a factory. Each male workers gets 5000 rupees and each female worker gets 2500 gets. Find the number of male workers in the factory ?

(a) 253 (b) 47 (c) 94 (d) 206

10. In what proportion must water be mixed with milk so as to gain 20% by selling the mixture at the cost price of the milk ? ( Assume that water is freely available )

(a) 1 : 4 (b) 1 : 5 (c) 1 : 6 (d) 1 : 12

Answers :

1. A 2. C

3. B 4. C

5. D 6. C

7. C 8. C

9. C 10. B

elitmus Question Paper

eLitmus Question Paper

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