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NMAT Ratio, Proportion and Percentages Questions
Ratio, Proportion and Percentages are among the most frequently tested arithmetic topics in the NMAT Quantitative Skills section. The section has 36 questions to be solved in 52 minutes, and these topics usually account for 3 to 4 of them directly. Since NMAT has no negative marking, every question you solve quickly and correctly adds straight to your scaled score.
Most NMAT Percentages questions rest on one idea: always identify the base before you calculate. Ratio and Proportion questions add another: every ratio is just a set of parts that scale by a common multiplier. Standard patterns include percentage increase and decrease, successive percentage changes, price and consumption problems, population growth, dividing an amount in a given ratio, combining two ratios, ages, incomes and expenditures, and direct and inverse proportion.
NMAT is a computer-adaptive test, so a strong start in core topics like Ratio, Proportion and Percentages helps you move to higher-difficulty questions. These concepts also drive Profit and Loss, Mixtures and almost every Data Interpretation set, so the time you invest here pays off across the paper.
Try to solve 10 to 15 Ratio, Proportion and Percentages questions daily. Mix direct percentage questions, successive change questions, ratio division questions, proportion questions and Data Sufficiency questions to build the pattern recognition you need to finish the Quant section on time.
NMAT Ratio, Proportion and Percentages Questions PDF
A single NMAT Ratio, Proportion and Percentages Questions PDF lets you practise every important pattern in one place instead of searching through books and websites. It also makes last-minute revision quick, since the formulas, fraction-percentage equivalents and solved examples sit together.
This PDF covers percentage change, successive percentage changes, price and consumption, population and depreciation, expressing one quantity as a percentage of another, dividing an amount in a given ratio, combining ratios, ages and income-expenditure ratios, mean and fourth proportional, direct and inverse proportion, and an NMAT-style Data Sufficiency question. Every question comes with a step-by-step solution so you can check both your answer and your method.
Solve the questions in a timed setting, aiming for about 1.5 minutes per question. After each set, go through the solutions and note where a fraction equivalent or the multiplier method could have saved time. Revisit the questions you got wrong after a few days to make sure the concept has stuck.
Download NMAT Ratio, Proportion and Percentages Questions PDF
How to Solve NMAT Ratio, Proportion and Percentages Questions
Here are some methods that can help you solve NMAT Ratio, Proportion and Percentages questions quickly and accurately:
Always fix the base first: Every percentage is a percentage of something. Before calculating, ask "per cent of what?" Most errors in percentage questions come from using the new value as the base when the question uses the old one, or the other way round.
Convert percentages into fractions: Fractions make calculation much faster than decimals. To find 37.5% of 640, use 3/8: 640 ÷ 8 × 3 = 240. Memorise the common equivalents:
- 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10
- 33.33% = 1/3, 16.67% = 1/6, 8.33% = 1/12
- 12.5% = 1/8, 37.5% = 3/8, 62.5% = 5/8, 87.5% = 7/8
- 14.28% ≈ 1/7, 11.11% = 1/9, 9.09% = 1/11
Use multiplying factors: An increase of 20% means multiply by 1.2, and a decrease of 15% means multiply by 0.85. For successive changes, simply multiply the factors one after another instead of recalculating the value at each step.
Treat ratios as parts: A ratio of 3: 5 means the quantities are 3k and 5k for some multiplier k. Write every ratio this way, and the question usually reduces to finding k.
Learn the key results by heart:
- Percentage change = (New value − Old value) ÷ Old value × 100
- A as a percentage of B = (A ÷ B) × 100
- Successive changes of a% and b% give a net change of a + b + (a × b) ÷ 100
- If A is r% more than B, then B is r ÷ (100 + r) × 100% less than A
- If price rises by r%, consumption must fall by r ÷ (100 + r) × 100% to keep expenditure the same
- Population after n years = P × (1 + r/100)^n; value after depreciation = P × (1 − r/100)^n
- To divide an amount in the ratio a : b, the shares are a ÷ (a + b) and b ÷ (a + b) of the total
- If A : B = m : n and B : C = p : q, then A : B : C = mp : np : nq
- Mean proportional of a and b = √(ab); third proportional to a and b = b² ÷ a; fourth proportional to a, b and c = (b × c) ÷ a
- Componendo and dividendo: if a/b = c/d, then (a + b)/(a − b) = (c + d)/(c − d)
Make the common term equal when combining ratios: For A: B = 2 : 3 and B: C = 4: 5, make B the same in both (12), giving A: B: C = 8: 12: 15.
Use the net change shortcut: A 20% increase followed by a 20% decrease gives 20 − 20 − (20 × 20) ÷ 100 = −4%, a net fall of 4%. This works for prices, salaries, populations and dimensions alike.
Eliminate options using the ratio sum: If two quantities are in the ratio 3 : 5, their total must be a multiple of 8. Use this to strike out options before you calculate.
Assume 100 when no value is given: If a question only talks about percentages, take the starting value as 100. It keeps every step in whole numbers.
For Data Sufficiency, do not solve fully: You only need to know whether a unique answer exists. A ratio alone never gives actual values, so check whether a statement supplies at least one real quantity.
Question 1
A group of 20 girls has average age of 12 years. Average of first 12 from the same group is 13 years and what is the average age of other 8 girls in the group?
correct answer:- 5
Question 2
The average of the 5 consecutive even numbers A,B,C,D ,E is 52.what is the product of B & E
correct answer:- 4
Question 3
Monthly salaries of Pia and Som are in the respective ratio of 5: 4. Pia, from her monthly salary, gives $$\frac{3}{5}$$th to her mother. 15% towards her sister’s tuition fees, 18% towards a loan and she shops with the remaining amount which was Rs. 2,100. What is the monthly salary of Som ?
correct answer:- 5
Question 4
Which of the following is a poetic composition of Kalidasa?
correct answer:- 3
Question 5
Prerna decided to donate 15% of her salary to an orphanage. On the day of donation she changed her mind and donated Rs. 1,896 which was 80% of what she had decided earlier. How much is Prerna's salary?
correct answer:- 3
Question 6
The difference between a two digit number and the number obtained by interchanging the two digits of the number is 9. If the sum of the two digits of the number is 15, then what is the original number?
correct answer:- 3
Question 7
A and B started a business with initial investments in the respective ratio of 18 : 7. After four months from the start of the business, A invested Rs. 2000 more and B invested Rs. 7000 more. At the end of one year, if the profit was distributed among them in the ratio of 2 : 1 respectively, what was the total initial investment with which A and B started the business?
correct answer:- 1
Question 8
Average score of a class of 50 students, in an exam is 34. Average score of the students who have passed is 52 and the average score of students who have failed is 16. How many students have failed in the exam?
correct answer:- 1
Question 9
A starts a small business with Rs. 3600. At the end of few months from the start of business, B joined the business with Rs. 4000. If the annual profit between A and B was divided between them in the respective ratio of 6 : 5, then B joined the business after how many months from the start of the business?
correct answer:- 5
Question 10
When 9 is subtracted from a two digit number, the number so formed is reverse of the original number. Also, the average of the digits of the original number is 7.5. What is definitely the original number ?
correct answer:- 1
Question 11
In a class, the respective ratio between the number of boys and the number of girls is 3:1. A test was conducted, wherein the average score of the boys was 73, while that of the entire class was 71. What was the average score of the girls?
correct answer:- 4
Question 12
Ratio of the earnings of A and B is 4 : 7 respectively. If the earnings of A increase by 50% and the earnings of B decrease by 25% the new ratio of their earnings becomes 8 : 7 respectively. What are A’s earnings ?
correct answer:- 4
Question 13
Average weight of three boys P, T and R is 54 1/3 kgs while the average weight of three boys, T, F and G is 53 kgs. What is the average weight of P, T, R, F and H?
correct answer:- 4
Question 14
A sum of money is divided among A, B, C and D in the ratio of 4 : 6 : 11 : 13 respectively, 1 the share of C is Rs. 7854, then what is the total amount of money of B and D together ?
correct answer:- 1
Question 15
The average age of a man and his son is 48 years. The ratio of their ages is 11 : 5 respectively. What will be ratio of their ages after 6 years ?
correct answer:- 4
Question 16
Sohail scored 33 marks in English, 37 marks in Science, 28 marks in Mathematics, 26 marks in Hindi and 32 marks in Social studies. The maximum marks a student can score in each subject in 60. How much percentage did Sohail get in this exam ?
correct answer:- 1
Question 17
In a test, minimum passing percentage for reserved and unreserved category is 40% and 54% respectively. A candidate from unreserved category secured 300 marks and failed by 24 marks. What are the minimum passing marks of reserved category in that test ?
correct answer:- 4
Question 18
Koel scored 49 marks in English, 37 marks in Science, 45 marks in Mathematics, 53 marks in Hindi and 55 marks in Social studies. The maximum marks a student can score in each subject is 70. How much approximate percentage did Koel get in this exam?
correct answer:- 3
Question 19
Nandkishore gives 35% of the money he had to his wife and gave 50% of the money he had to his sons. Remaining amount of Rs 11,250 he kept for himself. What was the total amount of money Nandkishore had ?
correct answer:- 2
