Ratios and Proportions Practice

• These notes are from an Objective Mathematics practice exercise
• The notes cover questions over ratios and proportions

Question 1

• Rs. 3200 is divided among A, B, and C in the ratio 3:5:8
• The difference between the share of B and C is Rs. 600

Question 2

• Rs. 94000 is divided among A, B, and C
• 20% of A's share = 25% of B's share = 15% of C's share
• C's share is Rs. 42000

Question 3

• Given a:b = 2:3, b:c = 1:2, and c:d = 3:1, the value of ab/cd is 1:2

Question 4

• Rs. 6400 is divided among three workers in the ratio 3/5 : 2 : 5/3
• The second worker's share is Rs. 3000.

Question 5

• In a class, there are 32 females
• The ratio of female to male students is 16:9
• The percentage of females in the class is 64%

Question 6

• Comparing the ratios 7:13, 17:25, 7:15, and 15:23 the lowest ratio is 7:15

Question 7

• Rs. 680 is divided among A, B, and C
• A gets 2/3 of what B gets, and B gets 1/4 of what C gets
• Their respective shares are: A gets Rs. 80, B gets Rs. 120, C gets Rs. 480.

Question 8

• In a rare coin collection, there is 1 gold coin for every 3 non-gold coins
• 10 more gold coins are added, resulting in a 1:2 ratio of gold to non-gold coins
• The total number of coins in the collection is now 90.

Question 9

• A bag contains Rs. 216 in the form of one-rupee, 50-paise, and 25-paise coins in a 2:3:4 ratio
• There are 114 50-paise coins

Question 10

• Three numbers are in the ratio 1/2:2/3:3/4
• The difference between the greatest and smallest numbers is 36
• The numbers are 72, 84, and 96

Question 11

• Two numbers are in the ratio 1 1/2 : 2 2/3
• When each is increased by 15, the ratio becomes 1 2/3 : 2 1/2
• The larger of the original numbers is 36

Question 12

• Given a/3 = b/4 = c/7, the value of (2a+3b+c)/b is 6.25

Question 13

• A bag has Rs. 51.25 in 2-rupee, 50-paise, and 25-paise coins
• The coins are in a 3:5:7 ratio

Question 14

• 177 is divided into 3 parts in the ratio 1/2 : 2/3 : 4/5
• The value of the second part is 45

Question 15

• Instead of dividing Rs. 117 among P, Q, R in the ratio 1/2 : 1/3 : 1/4, its divided in the ratio 2:3:4
• Both Q and R gained in the transaction by mistake

Question 16

• A mixture contains milk and water in the ratio 5:1
• 5 litres of water are added, and the ratio becomes 5:2
• The quantity of milk in the original mixture is 25 litres

Question 17

• There are three bottles of equal capacity with milk and water mixtures in the ratios 2:1, 3:7, and 4:11
• The bottles are emptied into a larger bottle
• The ratio of milk to water in the large bottle is 37:53

Question 18

• A's money to B's money is 4:5 and B's money to C's is 2:3
• A has Rs. 1000
• The total amount of money among A, B, and C is Rs. 4125

Question 19

• A watermelon is cut into two pieces in the ratio 3:5 by weight
• The bigger piece is further cut in the ratio 5:7 by weight
• The ratio of each of the three pieces is 36:25:35

Question 20

• The present ages of Anju and Sandhya are in the ratio 13:17
• Four years ago, the ratio of their ages was 11:15
• The respective ratio of their ages six years from now will be 7:8

Question 21

• If a tray containing a dozen glasses is dropped then 3:2 can not be the ratio of the broken glasses to unbroken glasses

Question 22

• If 2x = 3y = 4z, then x:y:z is 6:4:3

Question 23

• Alloys A and B contain gold and copper in the ratios 7:2 and 7:11, respectively
• Equal quantities of alloys A and B are melted to form alloy C
• The ratio of gold to copper in alloy C is 7:5

Question 24

• The fourth proportional to 72, 168, and 150 is 350

Question 25

• A person distributes pens among four friends A, B, C, and D in the ratio 1/3:1/4:1/5:1/6
• The minimum number of pens the person should have is 57

Question 26

• Of the given ratios, 1:2 cannot be the ratio of boys to girls in a school having 72 students

Question 27

• Given 4a = 5b and 7b = 9c, then a:b:c = 45:36:28

Question 28

• Of 120 applicants for a post, 70 are male and 80 have a driver's license
• The ratio between the minimum to maximum number of males having a driver's license is 1:2

Question 29

• Salaries of P, Q, and R were in the ratio 3:5:7
• Their salaries increased by 50%, 60%, and 50% respectively
• Their new ratio of salaries will be 3:6:7

Question 30

• Two alloys have Iron and Copper in the ratios 4:3 and 6:1
• 14 kg of the first alloy and 35 kg of the second alloy are mixed
• The ratio of copper to iron in the new alloy is 11:38

Question 31

• A bag contains one rupee, half rupee and ten paise coins
• The rupee and half rupee coins are in the ratio 2:5
• The half rupee and ten paise coins are in the ratio 4:9
• The total amount is Rs. 1125, so the number of coins of each kind is; 500, 1000, 2000

Question 32

• An employer reduces the number of his employees in the ratio 9:8 and increases their wages in the ratio of 14:15
• If the old wage bill was Rs. 1890, then the new wage bill is Rs. 1960

Question 33

• x is directly proportional to y
• y = 7 when x = 15
• the value of x when y = 14 is 30

Question 34

• x^2 varies directly as y^3; when x = 6, y = 3
• The equation that correctly represents this relationship is 3x^2 = 4y^3

Question 35

• The ratio of Mona's and Vikas's present ages is 9:10
• After 4 years, the ratio of their ages becomes 11:12
• Mona's present age is 18 years

Question 36

• A is 40 years old; B is 60 years old
• 10 years ago, the ratio of their ages was 3:5.

Question 37

• Three years ago, the ratio of a father and daughter's ages was 3:1
• 2 years hence, their ages will be in the ratio 22:9
• The ratio of their present ages is 5:9

Question 38

• Lalit's present age is three years less than twice his age 12 years ago
• Pankaj's present age to Lalit's present age is in the ratio 4:9
• Pankaj's age after 5 years will be 17 years

Question 39

• Three years hence, a boy's age will be 4 times the square of what it was 11 years ago
• The present age of the boy is 13

Question 40

• Raman, Manan, and Kamal are partners in a business
• Raman invests 2/5 of total, Manan invests 3/8 of total
• The ratio of profit for Raman, Manan, and Kamal is 16:15:9