Who has not fought over the last slice of pizza to divide it into equal portions? Ratio and proportion is not only an important part of daily chores but also forms an integral part of the Mathematics syllabus for both scholastic and competitive exams like GMAT, SAT Subject Test, SSC, etc. Understanding concepts pertaining to ratio and proportion thus becomes important as it will not only help you score well in the examination but will equip you to deal with proportions and quantities in day to day life. Here are some ratios and proportion questions that you can practice to have a better grip over the topic!
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What is Ratio?
The ratio is nothing but the simplest form or comparison of two related numbers. A ratio is a number that represents one quantity as a fraction of another item. For instance, the ratio of two integers 5 and 6 is 5:6. It also represents the number of times one quantity equals another. The “terms” refers to the numbers that make up the ratios. The higher portion of the ratio (numerator) is referred to as the antecedent, while the lower part of the fraction (denominator) is referred to as the consequent or descendant. For example, if the ratio is 4:6, then 4 is the antecedent and 6 is the consequent.
What is Proportion?
The proportion is denoted by ‘::’ or ‘=’. If the x:y ratio equals the a:b ratio, then x,y,a,b are in proportion. It is denoted by the symbols x:y=a:b or x:y:: a:b. When four words are in proportion, the product of two intermediate values (i.e., the second and third values) must equal the product of two extremes (i.e., first and fourth values).
Important Properties for Ratio and Proportion Questions
Here’s a quick sum-up of all the important properties that students must keep in mind while solving the ratio and proportion questions:
|Componendo and dividendo||If x:y=a:b then x+y:x–y=a+b:a-b|
|Invertendo||If x:y=a:b, then y:x=b:a|
|Alternendo||If x:y=a:b then x:a=y:b|
|Componendo||If x:y=a:b then x+y:x=a+b:a|
|Dividendo||If x:y=a:b then x-y:a=a-b:a|
|Subtrahendo||If x:y=a:b then x-a:y-b|
|Addendo||If x:y=a:b, then x+a:y+b|
Quick Tips and Tricks for Ratios and Proportions Questions
Here is a list of some important tips and tricks which will help students to solve ratio and proportion questions quickly:
- The ratio between two quantities should exist with the same kind.
- While comparing two ratios, their units must be similar.
- Significant order of terms must be there.
- If the ratios are equal to a fraction, then only a comparison of 2 ratios can be performed.
- If a/b=x/y, then ay=bx
- If a/b=x/y, then a/x=b/y
- Suppose a/b=x/y, then b/a=y/x
- If a/b=x/y, then (a+b)/b=(x+y)/y
- If a/b=x/y, then (a-b)/b=(x-y)/y
- Suppose a/b=x/y, then (a+b)/(a-b)=(x+y)/(x-y)
- If x/(y+z)=y/(z+a)=z/(x+y) and x+y+z is not equal to 0 then x=y=z
Ratio and Proportions MCQs
- The two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
A. 2 : 5
B. 3 : 5
C. 4 : 5
D. 6 : 7
- A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share?
A. INR 500
B. INR 1500
C. INR 2000
D. None of the above
- Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
A. 2 : 3 : 4
B. 6 : 7 : 8
C. 6 : 8 : 9
D. None of these
- In a mixture of 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is:
A. 20 L
B. 30 L
C. 40 L
D. 60 L
- The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls by 20% and 10% respectively, what will be the new ratio?
A. 8 : 9
B. 17 : 18
C. 21 : 22
D. Cannot be determined
- Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit’s salary?
A. INR 17,000
B. INR 20,000
C. INR 25,000
D. INR 38,000
- The sum of the three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
- The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
A. 3 : 3 : 10
B. 10 : 11 : 20
C. 23 : 33 : 60
D. Cannot be determined
- If 40% of a number is equal to two-third of another number, what is the ratio of the first number to the second number?
A. 2 : 5
B. 3 : 7
C. 5 : 3
D. 7 : 3
- Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
Ratio and Proportion Questions Worksheet
- Rohan, Rajesh, Rahul, and Raj are 4 brothers, and a particular sum of money has to be disbursed amongst them. This has to be done in 5: 2: 4: 3 proportion. Find out the share of Rajesh if Rahul gets Rs. 1,000 more than Raj.
- Siya made 60 litres of lemon soda. In this, the ratio of water and soda was 2:1. Calculate the total quantity of water that will make the ratio 1:2.
- There are 2 numbers, the ratio of which is 5:9. Upon adding 9 to the greater number and subtracting 5 from the smaller, the greater number becomes 3 times the smaller. Find out the 2 numbers.
- What will be the ratio of a square’s diagonal which has a side of 40 cm?
- The ratio of the business class and economic class in an airline between two stoppages is 6:4 and the total number of passengers travelling from business and economic class is 1:30. If Rs. 2,100 is taken as a fare for economic class, what will be the fare for business class?
- A mother was supposed to divide Rs. 390 amongst her 3 daughters, Riya, Jiya, and Siya such that thrice Riya’s share, twice Jiya’s share and 4 times Siya’s share will be equal. Calculate each sister’s share.
- A coin with a weight of 20 decigrams is worth Rs. 4,800. What will be the price of a diamond of a similar kind weighing 8 decigrams? Remember, the gold coin cost will vary as the square of its weight.
- Ramesh and Suresh are two friends. Ramesh received an appraisal of 10% and Suresh received a 20% appraisal. If their previous salaries were in the ratio of 4:5, calculate their revised salaries.
- In the purse of an old lady, there were 300 coins of the denominations 2 rupees, 5 rupees, and 10 rupees. Their total value is in the ratio 10:4:2. You need to find out the total number of coins of each type.
- Mr Kapoor divided Rs. 1,870 amongst his 3 grandchildren such that half of the first part was given to A, one-third of the second went to B, and one-sixth of the part given to C are equal. What is the amount given to each kid?
- X and Y are two alloys of Gold and silver made by putting together metals in the quantity 7:2 and 7:11 respectively. If exact quantities of two alloys are melted to make the third alloy named Brass, then what will the proportion of Gold and Silver in Brass be?
- At a party, Sachin was given a task to distribute Rs. 500 amongst Rishabh, Sahil, Sakshi, and Srishti such that Rishabh and Sahil get 3 times as much as Sakshi and Srishti together. Sahil gets 4 times what Rishabh gets and Rishabh gets 1.5 times as much as Sakshi. How much money does Sahil have?
- A cocktail contains water and alcohol in the ratio 4:3. If 5 litres of alcohol is added to the drink, the ratio becomes 4:5. Determine the quantity of water in the alcohol.
- In a piggy bank, there were Rs. 206 in the denominations of 10 rupees, 5 rupees, and 2 rupees coins in a ratio of 5:9:4. Determine the number of each type of coin.
- From the total strength of the class, if the no of boys in the class is 5 and no of girls in the class is 3, then find the ratio between girls and boys?
Ratio and Proportion Questions PDF
Ratio and Proportion PPT
The PPT below will make the topic clearer.
In order to score well in Ratio and Proportion questions, a lot of practice is thus required! Stream selection as well as choosing the right career path after class 12th are crucial decisions. Hence, you must seek guidance through experts in the field. Reach out to our experts at Leverage Edu who will provide guidance in not only choosing the career path that matches your interests but will also help you in sorting out the admission process for pursuing higher education abroad!