Download the BYJU'S Exam Prep App for free CAT preparation videos & tests - Download the BYJU'S Exam Prep App for free CAT preparation videos & tests -

Test Miscellaneous Arithmetic- Questions

1) A bottle contains 100% phenyl. 1/3 of it is replaced with water. The operation is repeated 4 times. What is the ratio of phenyl : water after the last operation?

a) 16:81

b) 1:5

c) 14:82

d) None of these

2) A mixture of 125 litres of milk and water contains 20% water. What amount of water needs to be added to this milk-water mixture in order to increase the percentage of water to 25% of the new mixture?

a) 7

b) 5.66

c) 8.33

d) None of these

3) There is a bottle of Coke. 25% of it is replaced by Pepsi. Again 25% is replaced by Pepsi and finally, another 25% is replaced by Pepsi. What is the approximate final percentage of Coke in the bottle?

a) 56

b) 52

c) 66

d) 42

4) Two casks contain mixtures of petrol (P) and kerosene (K). In the first cask P:K = 7:3 and in the second cask P:K = 3:1.In what ratio should the mixtures from the two casks be taken to give a mixture in which P:K is 11:4?

a) 2:3

b) 2:2

c) 1:2

d) 1:3

5) A rice trader sells one type of rice at Rs 2.70/ kg and loses 10%. He sells another type of rice at 4.5/kg and gains 12 ½ %. His objective is to mix these two types and sell the mixture at 3.95/kg and get a profit of 25%. What should be the ratio of quantities of rice mixed?

a) 23:6

b) 84:16

c) 6:1

d) None of these

6) A student finds the average of 10 positive integers. Each integer contains two digits.By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one.What was the difference between the two digits a and b?

a) 2

b) 4

c) 6

d) None of these

7) C and D are the children of A&B, who are married to each other. D is 5 years younger than C.Five years ago, A was twice as old as C. The current age of B is the average of A and C’s ages. If the average age of all of them is 34 years, find the current age of D?

a) 18

b) 21

c) 22

d) 27

8) Arun invests in bonds worth Rs. 40000 and he receives a 15% interest per annum. How much money should he invest in bonds that give 10% per annum so that he gains an overall 12% per annum?

a) 50000

b) 65000

c) 60000

d) 62500

9) The average weight of a group of 8 girls is 50 kg. If 2 girls R and S replace P and Q, the new average weight becomes 48 kg. The weight of P = Weight of Q and the weight of R = Weight of S. Another girl T is included in the group and the new average weight becomes 48 kg. Weight of T = Weight of R. Find the weight of P?

a) 48

b) 52

c) 46

d) None

10) Disha wants to paint her room a unique brown. For that, she uses a certain violet paint which contains 30 % blue pigment and 70 % red pigment by weight. She mixes that violet paint with a certain green paint which contains 50 % blue pigment and 50 % yellow pigment. When these paints are mixed to produce the brown paint which she uses, it contains 40 % blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?

a) 2.8 gms

b) 3.5 gms

c) 4 gms

d) 5.3 gms

11) A set S of real values consists of the following 5 elements, {4, 8, 12, 16, x} in any order. For how many values of x does the mean of set S equal the median of set S?

a) 0

b) 1

c) 2

d) 3

12) The average age of ‘n’ persons is 55. Two persons aged 41 and 47 respectively leave the group and three new persons aged between 60 and 65 join the group. If the average age of the group goes up by one year and if the initial number of people in the group is a multiple of 7, what is the number of persons now in the group?

a) 42

b) 43

c) 44

d) 45

13) Manju, who works at Ganesh Fruit Juice Centre, prepares 51 glasses of milkshake in 4 min, 18 sec in his first shift. After having a sandwich, he prepares 73 glasses in 7 min 13 sec. After another sandwich, he prepares 112 glasses in 12 min, 24 sec. The container in which the milkshake is prepared contains a maximum of 9 glasses of a drink at a time. Find his approximate average time of preparation of one container of the drink, if he starts with a fresh container each time.

a) 48 s

b) 50 s

c) 40 s

d) 51 s

14) There is a bag with a mixture of sugar, rice and wheat grains. The quantity of rice is 4/5th that of wheat and the quantity of sugar is 3/4th that of rice. In 12 kg of the mixture how much wheat and sugar will be there?

a) 7 kg

b) 10 kg

c) 8 kg

d) None of these

15) At a gold shop’s annual promotion, gold coins are distributed with each purchase. The higher the purchase, the higher the value of the gold coin. The value of the gold coin is directly proportional to the thickness & the square of the diameter. Two gold coins are given to a customer. The value of coin 1: coin 2 =4:1. The diameter of the coins is in a ratio 4:3. Find the ratio of the thickness of the coins?

a) 9:6

b) 11:7

c) 9:4

d) 12:5

16) There are 5 friends in a class who get marks in the ratio 3:4:5:6:7. the maximum marks are the same in each case. The total marks obtained by the 5 are 3/5th the maximum obtainable marks. How many friends got more than 70% of the total marks?

a) 1

b) 2

c) 3

d) 4

17) The charges for a graphics designer are partially fixed and partially variable with the number of hours. The charge is Rs 550 for 4.5 hours and Rs 300 for 2 hours. Find the charges of 1 hour?

a) 100

b) 200

c) 300

d) 400

Questions 18-19

In Little flowers school, for a school drill, the students are divided into 2 groups of lilies and daisies. The ratio of lilies: daisies = 8:3. the ratio of boys: girls is 7:4. 60% of the Daisy group is boys.

18) What is the ratio of the number of girls in the lily group and the number of boys in the daisy group?

a) 20:13

b) 11:20

c) 14:9

d) cannot be determined

19) What is the difference between the number of boys who are in the lily group and the number of girls in the daisy group, given that there are 48 girls in the daisy group?

a) 200

b) 240

c) 160

d) None of these

20) Till the age of 21, Arun grows such that his height varies as the square root of his age. When Arun is 9 years old, his height is 4 feet. What is his height at 16 years?

a) 5 feet

b) 5 feet 4 inches

c) 6 feet

d) 6 feet 2 inches

21) The height of an apple tree is given by the sum of two terms. The first term is directly proportional to the weight of the tree and the second term is directly proportional to the square of the weight of the tree. The height of the tree was 6 m and 8 m when its weight was 40 kg and 50 kg respectively. Find the approximate weight of the tree when its height was 5 m.

a) 39 kg

b) 25 kg

c) 32 kg

d) 35 kg

22) A picnic invites two kinds of charges: bus fare, which is independent of the number of people attending the picnic and buffet lunch, which increases directly with an increase in the number of people. The charges are calculated to be Rs. 165 per head when there are 200 invitees and Rs. 170 per head when there are 150 invitees. What would be the charges per head when there are 100 invitees?

a) Rs.175

b) Rs.180

c) Rs.185

d) Rs.190

23) Praveen buys two cans of milk from a manufacturer. The two cans are diluted to the same extent. To can 1 Praveen replaces 10 litres of the solution with pure milk and the concentration of milk becomes twice what it was. To can 2 he replaces 20 litres with pure milk, what is the ratio of the concentration of can 1 initially to that in can 2 finally.

a) 1:1.5

b) 1:2

c) 1:3

d) Cannot be determined

24) The receipts on railway travel vary as the excess of the speed of the train is over 30 kmph. The expenses vary as the square of that excess. What is the speed at which the profits will be greatest if at 60 kmph is the expenses are just covered?

a) 40

b) 35

c) 45

d) None of these

25) There are 3 types of Coffee powder available at La Café. They are graded based on the chicory content. The three grades of coffee contain 1% chicory, 2% chicory and 3% chicory in the coffee blend. If p kgs of the 1% grade and q kgs of the 2% grade and r kgs of the 3% grade are mixed to give p+q+r kgs of 1.5% grade, what is p in terms of q and r?

a) q+3r

b) (q+r)/4

c) 2q + 3r

d) 4.5q+3r

Visit Miscellaneous Arithmetic Solutions to check the detailed solutions of the given questions.