Numerical Reasoning Questions for NATA with Solutions 2026

Quick Answer: NATA numerical reasoning questions test mathematical and analytical ability through topics like percentages, ratio, speed-distance, geometry, and logical number problems. Based on NATA previous year papers, most questions are formula-based, moderate in difficulty, and focus on quick calculations and logical thinking.

Preparing for the National Aptitude Test in Architecture (NATA) requires a clear understanding of different sections, and one of the most crucial parts is the NATA Numerical Reasoning Questions. Unlike normal mathematics, numerical reasoning helps apply mathematics in a realistic context.

In the National Aptitude Test in Architecture, you can expect 10-12 questions based on numerical reasoning.

To ease your preparation, we have provided some of the important numerical reasoning questions for NATA 2026 exam here.

In this blog, we will discuss the importance of NATA Numerical Reasoning Questions, their types, strategies to solve them, and preparation tips to score well in this section.

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What are Numerical Reasoning Questions in NATA 2026?

Numerical reasoning in NATA syllabus refers to questions that test a candidate's basic mathematical ability, logical thinking, and problem-solving skills. These questions are designed to evaluate how quickly and accurately you can work with numbers, patterns, and real-life calculations.

The NATA Numerical Reasoning Questions hold significant weightage in the overall exam. Since architecture demands strong analytical ability and problem-solving skills, mastering this section ensures that students can think critically and handle complex design problems in their professional journey.

In the NATA exam, numerical reasoning is part of the Aptitude section (Part B) and typically includes formula-based and logic-based mathematical questions rather than complex calculations.

Based on previous year NATA papers, numerical reasoning questions commonly focus on speed, accuracy, and conceptual clarity rather than advanced mathematics.

Common Types of Numerical Reasoning Questions in NATA

• Averages
• Ratio and proportion
• Percentages
• Speed, time and distance
• Geometry and mensuration
• Number series
• Basic algebra
• Time and clock problems

Read more: Logical reasoning questions and answers for NATA Exam

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Important Topics in NATA Numerical Reasoning (With Difficulty Level)

Based on NATA 2022 & 2023 previous year papers, numerical reasoning questions are mostly formula-based. Common questions include averages, ratios, geometry, speed-distance, and logical number problems.

NATA Numerical Reasoning Important Topics & Difficulty Level

Topic	Frequency (Past Papers)	Difficulty Level	Example Question Type
Averages	High	Easy	Average of numbers
Ratio & Proportion	High	Easy-Moderate	Mixture, distribution
Percentage	High	Easy	Percentage increase/decrease
Speed, Time & Distance	High	Moderate	Train, race, bridge problems
Time & Work	Medium	Moderate	Work completion problems
Mensuration (2D & 3D)	High	Moderate	Area, volume, surface area
Geometry (Triangles, Polygons)	High	Moderate	Angles, perimeter, area
Number System	Medium	Easy–Moderate	Digit, number logic
Algebra (Basic equations)	Medium	Moderate	Simple equations
Clock & Time	Low–Medium	Easy	Clock coincidence problems
Profit & Loss	Low	Easy	Basic calculation problems
Series & Patterns	Medium	Easy–Moderate	Number pattern logic

NATA numerical reasoning focuses on Class 8-10 level mathematics, so strong basics and formula revision are enough to score well.

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NATA Numerical Reasoning Questions Practice - Use CreativEdge Free Resources 2026 Strategically

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Sample NATA Numerical reasoning Questions with Solutions for 2026 Exam

We have provided a few sample questions for your reference here to help you understand the type of questions asked from the numerical reasoning.

These questions are curated from the previous year's questions papers for NATA. Practising these questions regularly will help you perform well in the upcoming exam.

Q) 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:

A)  27

B) 33

C) 49

D) 55

Solution:

Let the two numbers be 3x and 5x, where x is a constant.

According to the problem, when 9 is subtracted from each number, the new ratio becomes 12:23. Therefore, we have the equation:

3x-9/5x-9 = 12/23

Now, cross-multiply:

23(3x−9)=12(5x−9)

Expand both sides:

69x−207=60x−108

Simplify the equation:

69x−60x=207−108

9x=99

Solve for x:

x=99/9=11

Now, substitute x=11 into 3x to find the smaller number:

3x=3×11=33

Answer: B) 33.

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Q) If 0.75 : x :: 5 : 8, then x is equal to:

A) 1.12

B) 1.2

C) 1.25

D) 1.30

Solution:

We are given the proportion:

0.75/x=5/8

To solve for x, we can use cross-multiplication:

0.75×8=5x

Simplify:

6=5x

Now, solve for x:

x=6/5=1.2

Answer: B) 1.2.

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Q) The salaries A, B, and 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

Solution:

Let the initial salaries of A, B, and C be 2x, 3x, and 5x respectively.

Now, the increments are as follows:

• A's salary increases by 15%, so A's new salary will be 2x+0.15×2x = 2.3x.
• B's salary increases by 10%, so B's new salary will be 3x+0.10×3x = 3.3x.
• C's salary increases by 20%, so C's new salary will be 5x+0.20×5x = 6x.

Express the new salaries as a ratio and simplify by removing the common factor x.

Preliminary Ratio = 2.3x : 3.3x : 6x

Removing x = 2.3 : 3.3 : 6

Multiplying by 10 to avoid decimals:

2.3*10 : 3.3*10 : 6*10

Thus, the new ratio is:

23 : 33 : 60

Answer: C) 23 : 33 : 60.

Read more: Short tricks to crack the NATA entrance exam on the first attempt

Q) If 40% of a number is equal to two-thirds 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

Solution:

Let the first number be x and the second number be y

We are given that 40% of the first number is equal to two-thirds of the second number:

0.40x=2/3y

To eliminate the decimals, multiply both sides of the equation by 10:

4x=20/3 * y

Now, multiply both sides by 3 to remove the fraction:

12x=20y

Divide both sides by 4:

3x=5y

Now, solve for the ratio x/y:

x/y = 5/3

Thus, the ratio of the first number to the second number is:

5:3

Answer: C) 5 : 3.

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Q) A team of three lumberjacks cut an average of 45,000 cubic feet of timber in a week. How many thousand cubic feet will seven lumberjacks cut in two weeks?

A) 21

B) 105

C) 225

D) 210

E) 22

Solution:

We are given that 3 lumberjacks cut an average of 45,000 cubic feet of timber in a week.

To find how much one lumberjack cuts in one week:

Timber cut by one lumberjack in a week=45,000/3=15,000 cubic feet = 15,000 cubic feet

Now, for 7 lumberjacks working for 2 weeks:

Total timber cut by 7 lumberjacks in 2 weeks=7×15,000×2=2,10,000 cubic feet

Since the question asks for the answer in thousands of cubic feet:

210,000/1,000 = 210

Answer: D) 210.

Read more: NATA Study Plan and Strategy

Q) A man covers a distance on a scooter. Had he moved 3kmph faster, he would have taken 40 min less. If he had moved 2kmph slower, he would have taken 40min more. The distance is

A) 30 km

B) 40 km

C) 45 km

D) 50 km

Solution:

Let the distance be d km, and let the original speed be v km/h.

The time taken to cover the distance d at speed v is d/v

Case 1: Speed increased by 3 km/h

When the speed increases by 3 km/h = (v + 3)

time decreases by 40 minutes = (t - (40/60)) hrs 

Therefore, distance d = (v+3) * (d/v - 2/3)

Case 2: Speed decreased by 2 km/h

When the speed decreases by 2 km/h = (v-2)

time increases by 40 minutes = (t + (40/60)) hrs

Therefore, distance d = (v-2) * (d/v + 2/3)

Now, we solve these two equations.

Step 1: Solve the first equation.

d = d - (2v/3) + (3d/v) - 2

(3d/v) - (2v/3) = 2 

Multiply both sides by 3,

(9d/v) - (2v) = 6

Step 2: Solve the second equation.

d = d + (2v/3) - (2d/v) - (4/3)

(2v/3) - (2d/v) = 4/3

Multiply both sides by 3,

2v - (6d/v) = 4

Step 3: Solve both equations.

Now, solve for d in both equations, set them equal, and find the value of v.

v = 12 km/hr

After solving for v, substitute it into one of the original equations to find d.

d = 40 km

Answer: B) 40 km.

Read more: Important GK questions for NATA exam

Q) 20, 19, 17, ?, 10, 5

A) 15

b) 14

C) 13

D) 12

Solution:

The given number series is: 20, 19, 17, ?, 10, 5.

To find the missing number, let's check the pattern of the differences between consecutive numbers:

• 20 to 19: Decrease by 1.
• 19 to 17: Decrease by 2.
• ? to 10: Decrease by 7.
• 10 to 5: Decrease by 5.

We see that the differences are: -1, -2, ?, -7, -5.

The missing difference between 17 and ? seems to be -3, based on the alternating pattern in the differences.

Thus, the missing number is:

17−3=14

Answer: B) 14.

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Q) An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point?

A) 6 hrs 30 min

B) 6 hrs 49 min

C) 6 hrs 45 min

D) 6 hrs 21 min

Solution:

Given:

• Distance to travel = 600 km
• Speed of the train = 100 km/h
• The train stops for 3 minutes after every 75 km.

Step 1: Calculate the time taken for travel without any stops.

The time to travel 600 km at a speed of 100 km/h is:

Time=Distance/Speed

=600/100=6 hours

Step 2: Calculate the number of stops made.

The train travels 75 km before stopping, and the total distance is 600 km. The number of stops made is:

Number of stops = 600/75−1=8−1=7 stops.

(The subtraction of 1 accounts for the fact that the train doesn't stop after the final segment.)

Step 3: Calculate the total time spent stopping.

Each stop lasts 3 minutes, so the total stopping time is:

Total stopping time=7×3=21 minutes.

Step 4: Calculate the total time taken.

The total time taken is the travel time plus the stopping time:

Total time=6 hours+21 minutes=6 hours21 minutes

Answer: D) 6 hrs 21 min.

Check: NATA Maths Syllabus

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Q) 12 men can complete work in 18 days. Six days after they started working, 4 more men joined them. How many days will all of them together complete the remaining work? 

A) 10 days

B) 8 days

C) 11 days

D) 9 days

Solution:

Given:

• 12 men can complete the work in 18 days.
• After 6 days, 4 more men join, so there are 16 men working now.

Step 1: Calculate the total work in man-days.

The total work in man-days is:

Total work=12 men×18 days=216 man-days

Step 2: Calculate the work done in the first 6 days.

In the first 6 days, 12 men work, so the work done is:

Work done in 6 days=12×6=72 man-days

Step 3: Calculate the remaining work.

The remaining work is:

Remaining work=216−72=144 man-days

Step 4: Calculate the number of days needed to complete the remaining work.

Now, 16 men are working on the remaining 144 man-days of work. The time required to complete the remaining work is:

Time=Remaining work / Number of men

144/16 = 9 days

Answer: D) 9 days

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Q) A two-digit number is three times the sum of its digits. If 45 is added to it, the digits are reversed. The number is 

A) 23

B) 32

C) 27

D) 72

Solution:

Let the two-digit number be represented as 10a+b

where:

• a is the tens digit,
• b is the ones digit.

First condition:

The number is three times the sum of its digits, so:

10a+b=3(a+b)

Expanding the equation:

10a+b=3a+3b

Simplifying:

7a=2b

Second condition:

If 45 is added to the number, the digits are reversed. So:

10a+b+45=10b+a

Simplifying:

10a+b+45=10b+a

a=b−5

Solving the system of equations:

a= 2, b=7

Thus, the number is:

27

Answer: C) 27.

Read more: Enhance your preparation with the best online coaching for NATA

Q) A square garden has fourteen posts along each side at equal intervals. Find how many posts are there on all four sides.

A) 56

B) 44

C) 52

D) 60

Solution:

Given that a square garden has 14 posts along each side at equal intervals, and we need to calculate the total number of posts on all four sides.

Since the posts are placed along the sides, there will be 14 posts on each of the four sides. However, the posts at the corners are shared by two sides. Therefore, we need to account for these corner posts only once.

• On each side, there are 14 posts, and there are 4 sides, so if we just multiply, we get:

4×14=56 posts

• But we have 4 corner posts that are counted twice, so we subtract 4 from 56 to avoid double-counting them:

56−4=52 posts

Answer: C) 52.

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NATA Numerical Reasoning 2026 - What Should be Your Preparation Strategy?

Strategy	What to Do	Why It Works
Focus on high-frequency topics	Prioritize ratio, percentage, geometry, mensuration, averages	These topics appear most often in NATA
Revise formulas daily	Memorize basic formulas for area, volume, percentages	Most questions are formula-based
Attempt easy questions first	Solve direct and quick questions first	Saves time and boosts confidence
Avoid lengthy calculations	Skip time-consuming problems initially	Improves accuracy and time management
Practice previous year questions	Solve NATA PYQs regularly	Helps understand question patterns
Improve calculation speed	Practice mental math and shortcuts	Reduces time per question
Maintain high accuracy	Attempt only confident questions	Accuracy matters more than attempts
Take timed practice sets	Practice with time limits	Improves exam performance

High-Scoring Topic Strategy

Priority	Topics	Preparation Strategy
High	Ratio, Percentage, Averages	Practice daily
High	Geometry, Mensuration	Revise formulas
Medium	Speed, Time & Distance	Practice frequently
Medium	Algebra, Number System	Focus on basics
Low	Complex calculations	Attempt only if easy

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Conclusion

Numerical Reasoning Questions for NATA are a vital component that tests an aspiring architect's mathematical prowess and logical problem-solving skills. These questions reflect the practical mathematical skills necessary in the field of architecture, ensuring candidates are well-prepared for the challenges they will face in their careers. By focusing on strengthening your mathematical foundation, practicing regularly, and utilizing various resources, you can excel in Numerical Reasoning Questions for NATA.

Remember, consistent practice and strategic preparation are the keys to mastering this section and boosting your chances of success in the exam. With diligence and the right approach, you can enhance your numerical reasoning abilities and pave the way for a promising career in architecture.

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