Answers to Aptitude and Numerical questions paper-1

You are here UCEED >> Solution to Numerical questions practice paper - 1

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In this post, I have covered answers/solutions for the numerical questions that I've included in my previous post - Numerical and aptitude questions for UCEED  for your reference. I have also added some additional aptitude questions at the end. Similar pattern might appear in your UCEED exam.

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1) 

Suppose a water tank is in the shape of a right circular cylinder is 20 meter long and 10 meter in diameter. How much sheet metal will be used in its construction. Picture shown below

Answer - 250*PI

Metal sheet required = surface area of the cylinder (PI*d*h)+ area of the two circles that are used to close the water tank (2*PI*sqrt(r))

 = PI*10*20 + 2*PI*sqrt(5)

 = 250*PI

2) 
A piece of wire of 42 cm long is bent into the shape of a rectangle whose width is twice its length. Find the dimensions of the rectangle.

Answer : L = 7, W = 14

3) 
A 10 meter pole casts a shadow of 5 meter. How tall is a tree with a shadow of 12 meter ?

Answer : 24

4) 
A man runs round a circular field of radius 14 meter at the speed of 88 m/hr. What is the time taken by the man to take twenty rounds of the field ? (take PI = 22/7)

Answer : 20hrs

5) 
A wire can be bent in the form of a circle of radius 7cm. If it is bent in the form of a square, then its area will be ? (take PI = 22/7)

Answer : 121 sqcm

6) 
A building of height 6 meter casts a shadow of 5 meter, then what will be the length of the stand post which casts 10 meter shadow

Answer : 12 m

7) 
A rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed for that ?

Answer : 56

Perimeter of the rectangle is 90+50+90+50 = 280, which when divided by 5 (because for every 5 meter a fencing pole is there) we get the number of poles
i.e. 280/5 = 56

8) 
If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that of the original square. Find the dimensions of the rectangle.

Answer : L = 24 cm, B = 10 cm

9) 
Next 2 numbers in the series 4,8,9,27 .....

Answer : its 4 sqr and 4 cube i.e 16,64

10) 
A metallic sphere of radius 3 cm is melted and recast into the shape of a cylinder of radius 3 cm, Find the height of the cylinder.

Answer : 4 cm

11) 
Metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single solid sphere. Find the radius of the resulting sphere

Answer : 12 cm

12) 
A 20m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22m by 14m. Find the height of the platform
(You may use calculator for this particular question, the main thing you need to understand is the concept )

Answer : 2.5

13) 
A rectangular sheet of dimensions 44 cm X 18 cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder.

Answer : 882*PI

please note the procedure
The given sheet is a rectangle with L=44cm and b=18 cm, so when we roll/fold along its length, it does mean that the new obtained cylinder will have height = breadth of the sheet (i.e 18 cm) and length of the sheet will now be the perimeter or circumference of the new cylinder. right ???

so,
h = 18 cm, and
2*PI*R = 44 cm which will give R = 7 cm,

now the volume of cylinder is PI*sqr(R)*h

14) 
An ant crawls from one corner of a room to a diametrically opposite corner along the shortest possible path. If the dimensions of a room are 3X3X3, what distance does the ant cover ?

Answer : sqrt(45)

If the sides of a cube are say a,b,c, then the shortest distance traveled by the ant from one bottom corner to diagonally opposite top corner is the minimum of

Sqrt[(a^2+b^2) + c^2], Sqrt[(b^2+c^2) + a^2], Sqrt[(a^2+c^2) + b^2]

In reality if u assume the box to be opened, then the two adjacent faces (on which the ant travels) will flatten to a rectangle shape with the length as (a+b) and width/height as c, now the shortest distance is the straight line joining the two points, i.e the diagonal which is obtained by using Pythagoras theorem.

The thing is the ant will crawl along from bottom point to the top diagonal by crawling along its wall. The ant will travel along two side walls, so instead of viewing that in 3D, We assume that the side wall in unfolded to the same plane as the first to from a 2D rectangle of bottom length = length of first wall + Length of second wall = a+b , and height equal to actual height of the solid cube. The shortest distance will now be the diagonal of he new rectangle.

15) 
There are 2 trees in a garden (say A and B) and on both the trees, there are some birds. The birds of tree A says to the bird of tree B that if one of you comes to our tree, then our population will be the double of yours. The birds of tree B tell to the birds on tree A that if one of you comes here, then our population will be equal to that of yours. How many birds are there in trees A and B ?

Answer : 7,5 birds

Let the no. of birds on tree A be "x"
and the no. of birds on tree B be "y"
so as per the first statement if one bird from B comes to tree A then no. of birds on A will be double of B". so
(x+1) = 2*(y-1)

as per the second statement "if one bird joins tree B from A, then the number of birds on both will be same ". So

(y+1) = (x-1)


now solve the above two equations for x and y.

16) 
A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm? 

Answer : 180 cm

The string is making 6 complete turns of height 108 cm, so for one complete turn it will cover 108/6 = 18 cm height

now assume we have a cylinder of height 18 cm and circumference 24 cm, if you unfold/unwrap the cylinder into a plain sheet, we will get a rectangle of width = height of cylinder and length of rectangle = circumference of the cylinder

Now the shortest length of the string is the diagonal of the rectangle which can be obtained by Pythagoras theorem i.e sqrt(18^2 + 24^2)

which will come to be 30 cm

so for a single turn it is 30cm, for the total 6 turns, length = 30*6 = 180cm

17) 

A creeper plant is climbing up and around a cylindrical tree trunk in a helical manner. The tree trunk has a height of 720 cm and a circumference of 48 cm.

If the creeper covers a vertical distance of 90 cm in one complete twist around the tree trunk, what is the total length of the creeper? (You may calculator for now, concept is important)

Answer : 816 cm

Applying the same concept as we applied for the prev question, we wil get the solution

It's already given that for one complete turn of the creep, the height is 90 cm, so just like previous problem we will unfold the cylinder to a rectangle of dimensions L = 48 cm and b = 90 cm

Finding the diagonal as sqrt(48^2 + 90^2) = 102 cm; which is the length of the creep for a single turn

Total number of complete turns = 720/90 = 8

So, the total length = 102*8 = 816 cm

18) 

There are 6 people in a room. They shake each other's hands once and only once. How many handshakes are there altogether?

Answer :  15 hand shakes

19) 

Your teacher has a total of 16 chalks. When a chalk reduces to 1/4 of its original size, it gets too small for her to hold for writing and hence she keeps it aside. But your teacher hates wasting things and so, when she realizes that she has enough of these small pieces to join and make another chalk of the same size, she joins them and uses the new chalk stick. If she uses one chalk each day, how many days would the 16 chalks last?

Answer :  21 chalks

Note the working as below

1.since the teacher uses one chalk a day, so for sixteen days 16 fresh chalks she uses

2. as stated in problem, every chalk leaves 1/4 th piece a day, so for 16 days she will have 16 pieces of 1/4th which she will join to get 4 chalks, got ? These four chalks she will use four more days

3. As usual for four days, the number of 1/4 piece left is 4, which she joins to get a single chalk

4. That chalk she will use the next day

So, summing them, we have 16+4+1 = 21 days

20) 
A snail can crawl 5 meters in 5 min, what will be the total distance covered by a group of 5 snails starting at the same time in 5 min ? 

Answer :  5 meters

21) 
Somu and Bhanu each have a collection of tennis balls. Somu said that if Bhanu would give him 4 of his balls they would have an equal number; but, if Somu would give Bhanu 4 of his balls, Bhanu would have 2 times as many balls as Somu. How many balls does Bhanu have?

Answer :  28 balls

The solution goes like this

Let the no. of balls with Somu be "x"

and the no. of balls with Bhanu be "y"

so as per the first statement "if Bhanu gives four balls to Somu, then both will have equal" so

(x+4) = (y-4)

as per the second statement "if Somu gives four balls to Bhanu, then Bhanu will have double than Somu ". So

(y+4) = 2*(x-4)

now solve the above two equations for x and y.

22) 
A tennis championship is played on a knock-out basis, i.e., a player is out of the tournament when he loses a match.

• How many players participate in the tournament if 85 matches are totally played ?
• How many matches are played in the tournament if 17 players totally participate?

Answer :  a-86, b-16

23) 
There are five different houses A to E. A is to the is to the right of B and E is to the left of C and right of A. B is to the right of D. Which of the houses is in the middle ?

Answer : D-B-A-E-C

24) 
Ram noticed in a cycle stand that there were a total of 14 bicycles and tricycles. If the total number of wheels was 35, how many tricycles were there?

Answer : 7

25) 
Suppose 6 monkeys take 6 minutes to eat 6 bananas, how many minutes would it take

• 3 monkeys to eat 3 bananas
• 24 monkeys to eat 24 bananas

Answer : 6, 6

6 monkeys - 6 min. - 6 bananas
1 monkey - 6 min. - 6/6 bananas ( = 1 banana) 
multiply by 3 
3 monkeys - 6 min, - 3*1 banana
simlary, multiply by 24
24 monkeys - 6 min, - 24*1 banana

Note that all the monkeys eat simultaneously, so, 6 monkeys together eat 6 bananas in 6 minutes, that means, a monkey can eat one banana in 6 min.
so, in the same time of 6 min, 'n' monkeys can eat 'n' bananas.

26) 
A snail creeps 8 ft up a wall during the daytime. After all the labor it does throughout the day, it stops to rest a while... but falls asleep!! The next morning it wakes up and discovers that it has slipped down 5 ft while sleeping. If this happens every day, how many days will the snail take to reach the top of a wall 29 ft in height?

Answer : 8 days

first day, the snail goes 8ft, but at night, it slips to (8-5) = 3ft
second day, it has to start at 3 ft and by the end of the day, it will have reached 3+8 =11ft, but at night it will slip to 5ft, thus totalling to 11-5 = 6ft
So, every at the end of everyday it will go 3ft height

At the end of 7th day, it would have climbed till, (3*6 + 8) = 26 ft, but at 7th day night, it might have fall down to 26-5 = 21 ft

on 8th day, it will reach 21ft + 8ft = 29ft, by then it has reached the top and so it doesn't have to slip down. So, the answer is 8 days


27) 
A 24 cm x 24 cm square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 25 nails on each side of the square. Each nail is at the same distance from the neighbouring nails. How many nails does the carpenter use?

Answer : 96 nails

28) 
A block of wood in the form of a cuboid 6cm × 4cm × 4cm has all its six faces painted pink. If the wooden block is cut into 96 cubes of 1cm × 1cm × 1cm, how many of these would have pink paint on them?

Answer : 80 cubes


Only those cubes at the surface of the cube will have the colored surface.
there will be 4 surfaces with sides 6cm x 4cm
and two surfaces of sides 4cm x 4cm

So, the total number of 1 X 1 cubes will be = 6*4*4 + 4 *4*2 = 128

But out of this, some cubes will be shared by adjacent surfaces, leke all the cubes at the eight corners of the cuboid will be shared by 3 surfaces (2 times counted extra for each corner cube), so for all these eight corners, we have to remove = 8*2 = 16
Also, there will be cubes at the sides/edges of the cuboid, which will be shared by two adjacent surfaces, like that there will be - (6-2)*4 + (4-2)*2*4 = 32

So, total will be 128 - 16-32 = 80

You can check detailed explanation for similar question in Question 2 of CEED 2015 answer key with solutions

29) 

In a classroom of 100 students, 40 students feel alert, while 60 students feel bored, if 50% of the alert students turn bored. After that, 50% of the bored students turn alert, what is the final number of students who feel alert and bored ?

a. 20 alert, 80 bored

b. No change - 40 alert, 60 bored

c. 60 alert, 40 bored (ans)

d. 50 alert, 50 bored

Explanation :

Initial step :
Alert = 40
Bored = 60

Step-1 :
50% of the alert students turns bored. so,
Alert = 40 - 40*0.5 = 20
Bored = 60 + 20(from alert) = 80

Step-2:
50% of the bored students turns alert
Bored = 80 (from previous step) - 80*0.5 = 40

Alert = 20 (from previous step) + 40 = 60

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Hope the above questions gave you some idea as well as helped you as part of your practice.


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how to prepare and what to practice for UCEED

You are here UCEED >> How to prepare and practice for UCEED

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Download PDF - complete UCEED links of SYL blog 

From 2020, UCEED started asking sketching questions too as part of Part B. So the below strategy on how to prepare will consider the sketching part too.

Quick video guide on what topics to start

Step 1:

I always recommend students to start attempting the latest previous paper - to understand the question paper pattern, which will help in understanding the type of questions being asked, the difficulty level, the ratio of analytical to Gk kind questions, and of course the sketching question type being asked. Assuming that you have considered giving UCEED or NID (After you've understood what exactly is design about, what will be career prospects for a designer and what will be career or job type after becoming a designer. If you are still not sure about this, I would suggest you check through the course content of B.Des as well as MDes. After you understand the course content, understand what exactly will be the role of a designer (general or specialized in some particular stream like say UI) as part of job. For this you can refer to youtube videos or read through the designers' role online.)

Assuming that you are damn sure that design is your thing and you are not taking this just to get away from engineering or to do something different from what others are doing, the first step, like I already mentioned above, would be in attempting the UCEED previous paper (at least one recommended, the more the better). Also, make sure that you attempt the sketching question. 

Step 2:

Based on your previous paper attempts, you want to list the following

• What exactly are the topics that you should focus on - as part of the preparation?
• What type of questions you feel comfortable and what questions you feel you need preparation?
• What is your current drawing/sketching level? Which part you are good and which part you are lacking?
• Do you actually need coaching for this or can you do self-study? If coaching needed, then is that only to improve sketching or also for part A?
• How fast you can pick up? how much time you should be spending weekly or monthly and what should be your preparation plan?

The list goes on. Since every individual capability varies, it is up to you to decide how you should strategize your preparation though people like me can give only a generalized suggestion. You need to modify by including or deleting topics or setting a timetable as the one shared by me or someone form whom you get help. I've already shared a timetable for Part A of UCEED. I will add a sketching part as well to that weekly strategy post but it's up to you to modify that and take up based on the phase at which you are picking up and based on your current commitments. 

Here is  - Weekly strategy and schedule/time-table for UCEED practice

I would say, with my experience, the following topics are what most of you need to start with:

1. folding and unfolding
2. imagination and visualization
3. mensuration basics and mensuration related aptitude
4. mechanical ability
5. more practice on non-verbal image-based reasoning
6. Observation and patterns finding
7. shadows and lighting 
8. paper folding, unfolding and cutting
9. perspective imaging/drawing and viewing

As part of starting with the above topics, I would suggest you start with the below links and go through them in order. Understanding the below will help you directly and indirectly with the above-listed topics: (below is the first set of links are just refreshers to help you start and check your state of imagination). 

What to start for design aptitude? 

How to solve design aptitude, non-verbal, and Ability questions with examples

Solid Manipulation - some tips on the unfolding of solids to improve imagination

Working with geometric objects

Solving no. of faces on solids

Solving tessellation problem

After you referred the above starters, maybe you can start practicing the listed topics above by finding sample questions and exercises in the below links

Image aptitude and non-verbal ability resource page

Design aptitude and reasoning resource page

(especially go through the guide and study material on geometry and solids related topics in the link above)

Complete UCEED Resource collection

Step 3:

Regardless of your sketching level, it's best to start with sketching practice. Now that you have understood the sketching question type being asked in the exam, you can take up similar questions and keep attempting them (I'm leaving a link to a set of several practice questions and free guide for Part B subjective of UCEED). In parallel, if you are a beginner (or average) in sketching, you need to start practicing the sketching as a starter. For this, you can follow the below steps 

1.  First few weeks - do copy sketching preferably with pencil. Take up some existing sketches from the internet like perspective sketches of buildings, indoors etc., objects like baskets, gadgets, appliances, including humans, etc. 
2. Apart from the above set of practice, you may also plan to sketch scenarios like that of an indoor activity, street activity, animals etc. This part can be done by copying the available sketches in the internet. You can find plenty of pencil sketches from google image searches. 
3. Also, you need to learn about the proportionate drawing of sketches - like the proportionate drawing of say a cat in comparison to a human or to say a laptop, etc. You need to learn on how to draw objects and express them incorrect sizes and proportions. You need lot of practice on this. Size and proportion are going to be very important.  For this, there are several online help available, including youtube. Most importantly, you should learn by observing and understanding the way of drawing in proportion. Practice is what you need. We cannot master overnight, right? be patient and keep practicing. 
4. Once you are confident enough that you are able to maintain proportion, perspective, ratios, and basics on line strokes, line quality etc., you can start sketching scenarios or objects (including humans and animals in a scene) out of your imagination. Assume some scenarios and try to sketch for that. I've also listed several questions as part B help. You can take them up weekly and try to attempt that. 
5. As you keep practicing the above, you will understand how fast/slow you are progressing and whether you are really picking up or not. If not satisfied and if you feel like you are not able to do without guidance, you might want to join a sketching tutorial classes. Even after the tutorials, if you are not able to pick up, maybe it's time to think whether design suits you or not! A good designer is one who needs to quickly express his imagined thoughts and communicate well to others, which needs sketching knowledge to an extent. So, you should make sure that you are taking this up out of passion and not for any other reason!

Step 4:

The discussions in step 3 are wholly about Part B's improvement. Apart from part B, there are certain things that you should take up parallelly to get ready for Part A as well.  

UCEED will probably be structured to test candidates' abilities. The ability could be any/all of mathematical, design, mechanical, observative, and imaginative nature. But, do remember that it is your 'common sense' that helps you the most! Common sense and practicality are what is needed even for every designer. So, while facing questions, do apply your common sense initially without going for theory or crude way of solving. If that doesn't turn out, and if the questions (other than GA) are like, they need some formula or something, then only look/try with the theory you know.

You might have observed that I stressed the importance of geometry and image-involved questions by including more questions/links related to solid manipulations in this blog's resource page. The reason is obvious, if you have a good grip on geometry manipulation, then you will definitely have good imaginative power. Observation, visualization, and imagination are mutually inter-related. These topics could be considered as a set. So, if you wish to improve your imagination (which included V and O) badly, then do try your hands on geometry and image type questions. If you have time, then take as many exercises as possible, (I have included many of them in the resource page or try from the internet or any books that you come across) and make yourself comfortable with these areas.

So, start your preparation by getting used to solving non-verbal and verbal kind of questions that are related to image, sequence, patterns, etc. that can enhance your observation skills.

Verbal Reasoning - Syllogism, Logical Sequence of Words, Series Completion, Cause and Effect, Dice, Venn Diagrams, Cube and Cuboid, Analogy, Seating Arrangement, Character Puzzles, Direction Sense Test, Arithmetic Reasoning

Non-Verbal Reasoning - Series, Analogy, Classification, Analytical Reasoning, Mirror Images & Water Images, Embedded Images, Pattern Completion, Figure Matrix, Paper Folding, Paper Cutting, Rule Detection, Grouping of Images, Shape Construction, Image Analysis, Cubes and Dice

English comprehension, language

By now, you must be aware that reading comprehension, synonymous, sentence completion, are some of the topics that have to be covered for UCEED. Practicing this from the very beginning is recommended for those who are average in English (like me).   You need to be fast in attempting language and comprehensive questions, which might consume much of your time during exam. There is no other option other than going through practice exercises. It's a fact that humans learn from experience and through practice!

General Awareness

Don't indulge yourself much into current affairs and GK studies. It's not worth spending much time on these topics that could consume much of your time for just some questions (unless you already have a good grip). Questions that cover general knowledge, current affairs, commonly used materials, designers, artists, animation (movies, technology, directors), etc require you to memorize and so it's better to focus on such topics at the end of the practice. I mean, plan these topics before a week (or so; based on your capability. I prefer two to three days before the day of the exam).

Let me tell you my case - why I did like that? even if I prepare and cover GA topics before a month (say), then also I will have to revise/recap the same topics sometimes near to the exam day, kind of double work! agreed? So that's why I planned and chose to study two days before the exam, (since I had ready-made materials, I didn't invest time for resource gathering, that's why felt confident of my two-day plan). Alas, it worked for me!

Let's discuss your case. If you have quite a good number of GA resources with you, and if you are like me - need recap even after going through those topics once or twice, then better stick with the plan of covering these topics before a week or so. Just make sure that you get hold of those materials, else you need to start gathering those topics (since no collections or books are available for UCEED). 

I've tried to cover as many topics as I can, in this blog, you may use that if you feel like you need more topics or more materials for the same topics hat is included in this blog, then better start gathering them by searching the web or in reference books.

Reasoning tests

Reasoning questions are just like brain teasers or it's kind of geometry type questions (we just saw (above) - how to deal with these topics). As far as possible, try practicing these questions every day, right from the day you started your practice. You cannot/should not expect to develop Reasoning and Imagination skills overnight! That is not recommended and of course not possible! 

 Design GA

Design GA in the sense - photography terms, logos, art and design-related terms, famous personalities, can be considered as a one-time study topics. So, these topics could be included in your regular time table. Like I mentioned earlier, since these topics are available, so there's little need for you to worry about the material collection. You may go for additional topics once you cover those that I have included as well as some other materials that you got somehow.

Environmental study 

I won't recommend stressing on these topics. Considering past years' paper pattern, it is evident that environmental study as listed in the syllabus is never asked or asked at the least. So, maybe you can target the other mandatory asked topics like the non-verbal and all.

UCEED video guide and discussion on the new pattern from 2020 

--------------------Skip reading the below discussion if your exam is nowhere near, especially if you are just starting your preparation------------------------

Time management during UCEED exam

I received a query from our blog friend, who wants to get a strategy for writing (during) UCEED exam, in the sense, which type of questions to attempt, how and in what system/order? In this regard, I just thought of sharing this with everyone, so that others would also benefit from this.

Timing and strategy in exams vary from person to person, It depends on how fast your solving skills are, which subjects you are good at, etc. Anyway, If you want to devise a plan by yourself during an exam, then you may check the following facts, considering them according to your own convenience --

Numerical questions (esp. puzzles and aptitude ques) are time-consuming while picture type questions are time savers (if you are able to solve them!). You may judge yourself whether your solution went correct or not (in most cases). That's why I insisted everyone to practice more on picture/geometry type questions so that you would save your time as well as help solve other similar questions, rather going on tail and error basis for others (like English, GA, etc) - which happens in most cases. Remember the negative marking feature in UCEED! (another reason being picture (image/geo) type questions opens your imagination skills). So, if you are really good at common sense type questions, then start working on them during the exam.

UCEED and CEED exams are conducted on-line. So, there is a provision to check

1. Which questions are answered
2. Which questions are marked for checking
3. Which questions are not answered

This helps you to navigate to the desired question as and when needed; within the time limit (within 3 hrs). So, I think it's not a problem if you leave behind some questions for later review. But make sure that you dedicate some time (at the end) to review the left behind questions or go through those questions that you haven't tried yet. I usually do like this - fortunately, most of the other exams have section-wise topics. So, I try the sections that demand trial and error features; as the last part. Most of the time I end up with just 15-10 mins, which of course is not a good practice though.

By practicing previous CEED papers as well as UCEED model papers, you should have understood your level. This should have given you an idea about which areas you are good at and which area you need development. Hoping that you tried your hands on the topics which you felt like needed development, you now know more about the subject and you can judge whether you are still lacking behind (need improvement) or you are able to pick up in course of time. If in case you are still stuck with some topics even after practice, then better leave those questions without attempting during the exam, but be sure that you are sufficiently prepared for other topics!

Negative marking is the biggest bothering feature in CEED as well as in UCEED. So unless you are not sure (probability is less than 50%), don't jump to answer those questions.

This is weird! I should have written on how to solve questions with tricks, but instead, I'm giving how to manage time and deal with negative markings. As the topics are diverse, it's difficult (and almost impossible) for anyone to cover each and every topic through blogs. So that's why you have to cover those topics (like different types of aptitude questions, etc) by yourself. I know this is not proper (giving time tricks), but since I had experienced the pain of over marking negatives in exams, I thought it would be better if you mind the questions properly.

My Final Tips for UCEED students (before the day of the exam)

Hope this is of some use to you!

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