# Models in Number Series

## Two-Three Level Depth

In this model we need to go for more than one level of subtraction. Sometimes it can be two or may be three. You should go on until you identify a proper pattern in the series. Here are few examples to understand this much better.

# Cognizant placement papers

## Cognizant Written Test Pattern

 Section Name Time Duration ( 55 Minutes) Number of Questions (55 questions) Quantitative Aptitude 16 16 Reasoning Ability 14 14 Verbal Ability 25 25

## Cognizant Placement Papers

1. Three cubes of edges 6 cms, 8 cms and 10 cms are melted without loss of metal into a single cube. The edge of the new cube will be:
a. 8cms          b. 12cms          c. 14cms          d. 16cms
Solution : As, the three individual cubes are melted into a single one the volume of the three cubes will be equal to the volume of the new large cube.

Volume of the new large cube = 63 + 83 + 103
Volume of the new large cube = 216 + 512 + 1000
Volume of the new large cube = 1728cm3
We know, Volume of a cube = edge3
1728 = edge3
12 = edge
Therefore, the edge of the single large new cube is 12cms.

2. In 24 minutes, the hour hand of a clock moves through an angle of:
a. 60°          b. 24°          c. 12°          d. 5°
Solution : We know, Hour hand makes $360^{\circ}$ in 12 hours, i.e In 1 hour it takes $30^{\circ}$.
If it takes $30^{\circ}$ in 60 minutes, then in 1 minute it takes $\frac{1}{2}^{\circ}$ .
Now, In 1 minute it takes $\frac{1}{2}^{\circ}$
then, in 24 minutes it takes $12^{\circ}$.
Therefore, Option B is the right answer

3. Four different electronic devices make a beep after every 30 minutes, 1 hour, 3/2 hour and 1 hour 45 minutes respectively. All the devices beeped together at 12 noon. They will again beep together at:
a. 12 Midnight          b. 3 AM          c. 6 AM          d. 9 AM
Solution : So, the four devices beep after 30 minutes, 60 minutes, 90 minutes and 105 minutes respectively.
Interval after which the devices will beep together is = LCM( 30, 60, 90, 105) minutes
They beep again after = 1260 minutes or 21 hours
so, if they beeped at 12 Noon after 21 hours or at 9 AM they again beep together.

4. The average of three numbers is 77.The first number is twice the second and the second number is twice the third. Find the first number?
a. 33          b. 66          c. 77          d. 132
Solution : Given Average = 77 and first = 2 (second) and second = 2 (third).

We know; Average = $\frac{Sum&space;of&space;numbers}{Number&space;of&space;numbers}$  and First : Second : : 2 : 1 and Second : Third : : 2 : 1

77 = $\frac{Sum}{3}$
first : second : third :: 4 : 2 : 1 [ using the combining the ratio shortcut]
Therefore, Sum = 231 and sum of the ratios is 4x + 2x + 1x = 7x
7x = 231
x= 33
Hence, the first number is 4x or substituting x = 33
First number = 4 * 33 = 132

5. If the number 7×86038 is exactly divisible by 11, then the smallest whole number in place of x?
a. 1          b. 2          c. 3          d. 4
Solution : We know, that the divisibility rule for 11 is [Sum of odd places] – [Sum of even places] = Should be divisible by 11 then the entire number is divisible by 11.
Using that, [ 7 + 8 + 0 + 8] – [x + 6 + 3]
23-x-9
14-x
The closest number to 14 which is divisible by 11 and less than 14 is 11. Hence, the smallest whole number in place of x is 3.

6. The sum of three consecutive natural numbers each divisible by 3 is 72. What is the largest among them?
a. 21          b. 24          c. 27          d. 30
Solution : We know, If the series is in Arithmetic Progression and if the number of terms in the series is odd then always the middle number is the average.
Here, in the question, there are 3 terms in the series(the number of terms are odd) and the series is in AP.
Average = $\frac{Sum}{Terms}$
Average = $\frac{72}{3}$
Hence Average is 24 or the middle number is 24.
Since, they are consecutive numbers divisible by 3. The numbers are 21, 24, 27. The largest among them is 27. Hence Option c is the correct answer.

7. If Shalu buys 6 more apples, his carton will weigh 14.5 kilograms. If the weight of one apple is 250 grams. How many apples did he initially had in his carton?
a. 58          b. 56          c. 54          d. 52
Solution :
Weight of 1 apple is – 250 grams
then weight of 6 apples = 250 x 6 = 1500 grams or 1.5kg
Initial Weight = Present weight – Weight of 6 apples
Initial Weight = (14.5 – 1.5)Kg
Initial Weight = 13kg
Number of apples in the carton initially= $\frac{Total\,&space;Weight}{Weight\,&space;of\,&space;each\,&space;apple}$
Number of apples Initially = $\frac{13000\,&space;grams}{250\,&space;grams}$
Number of apples Initially = 52
Otpion D is the correct answer

8. A tailor has 37.5 meters of cloth and he has to make 8 pieces out of a meter of cloth. How many pieces can he make out this cloth ?
a. 300          b. 360          c. 400          d. 460
Solution : Length of each piece = $\frac{1\,&space;meter}{8\,&space;pieces}$ = 0.125 meters (because the questions says 8 pieces out of a meter)
Required number of pieces = $\frac{37.5}{0.125}$ = $\frac{375*100}{125}$ = 300 pieces

9. By what number should be 86700 divided to make it a perfect square?
a. 300          b. 360          c. 400          d. 460
Solution: The prime factorization of 86700 is
17 x 17 x 3 x 100
Now, other than the ‘3’ in the prime factorization 17 and 10 have squares. Hence if we can remove 3 from the number the rest of the number is going to be a perfect squrare. So, the number should be divided by 3.

10. Which is the Closest approximation to the product
0.3333 x 0.25 x 0.499 x 0.125 x 24 ?
a.  $\frac{1}{8}$          b.  $\frac{3}{4}$          c.  $\frac{3}{8}$          d.  $\frac{2}{5}$
Solution : 0.3333 can be written as $\frac{1}{3}$ , 0.25 as $\frac{1}{4}$ , 0.125 as $\frac{1}{8}$ and 0.499 as $\frac{500}{1000}$ or $\frac{1}{2}$
Now, $\frac{1}{3}\:&space;*\:\frac{1}{4}\:&space;*\:&space;\frac{1}{2}\:*\:&space;\frac{1}{8}\:&space;*\:&space;24$
$\frac{1}{8}$ is the approximated value.

11. The difference of two numbers is 11 and one fifth of their sum is 9. The numbers are :
a. 31, 20          b. 30, 19          c. 29, 18          d. 28, 17
Solution:

Method-1 (Using Equations)

Let the two numbers be a and b.
a – b = 11 — eq(1)
(a+b)* $\frac{1}{5}$ = 9
a + b = 45 — eq (2)
2a = 56
a = 28 and b = 17

#### Method -2 (Using Option Elimination)

The question says one-fifth of the sum of the numbers, which means their sum is divisible by 5. The divisibility rule for 5 is unit’s place should be 0 or 5.
Let us observe the unit digit of their sum.
Option a- 31 + 20 = 1 in the unit place. Hence, not divisible by 5, therefore, not the answer.
Option b- 30 + 19 = 9 in the unit place. Hence, not divisible by 5, therefore, not the answer.
Option c- 29 + 18 = 7 in the unit place. Hence, not divisible by 5, therefore, not the answer.
Option d- 28 + 17 = 5 in the unit place. Hence, divisible by 5, therefore, This is the right answer.
Note : If there are two options where there sum are divisible by 5, then check the other two conditions as well i.e one-fifth should be 9 and difference between the numbers should be 11.

12. How many numbers between 1 and 100 are divisible by 7 ?
a. 9          b. 11          c. 17          d. 14
Solution: Lets go for option elimination, We should be looking for the largest number from the options and the answer should be closer to 100
Say, option a – 9 numbers are divisible between 1 and 100. Then 9 x 7 = 63 (close to 100)
option b – 11 numbers are divisible between 1 and 100. Then 11 x 7 = 77 (closer to 100)
option c – 17 numbers are divisible between 1 and 100. Then 17 x 7 = 119 (Beyond 100) which means, 17 is the wrong answer
option d – 14 numbers are divisible between 1 and 100. Then 14 x 7 = 98 (Closest to 100)
Hence, 14 is the right answer

12. 7. What is the number which when multiplied by 13 is increased by 180?

#### Method-1 (Using Equations)

Let the number be X
X * 13 = 180 + X
12X = 180
X= 15
Hence, the number is 15

#### Method -2 (Using Option Elimination)

According to option – a, if the number is 13 multiplied with 13 = 169< 180. Not satisfying the condition in the question. Hence, it is te wrong answer.
Option – b, 15 multiplied with 13 = 195 which is 180 more than the number (15). Satisfying the condition in the question. Hence Option B is the right answer.

13. A person travels 48 kms at 12 kms/hour and further 48 kms at 16kms/hour. His average speed for the whole journey is ?
a. 14          b. 13 $\frac{4}{7}$          c. 12 $\frac{5}{7}$          d. 13 $\frac{5}{7}$
Solution: We know, When same distance is traveled in both the situations then the average speed is $\frac{2\,&space;*\,&space;a\,&space;*\,&space;b}{a\,&space;+\,&space;b}$

Here, the distance traveled in both the scenarios is 48kms.
Applying the formula —  $\frac{2\,&space;*\,&space;12\,&space;*\,&space;16}{12\,&space;+\,&space;16}$
$\frac{6\,&space;*\,&space;16}{7}$

13 $\frac{5}{7}$

14. When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?
a. 0          b. 5          c. 2          d. 3
Solution: According to the question, the integer n = (q * 8) + 3, where q is the quotient and 3 is the remainder.
Now, 6n = (q * 8 * 6) + 3 * 6
i.e 6n = 48q + 18. Now, when this number is divided by 8 ;

$\frac{48q}{8}\:&space;+\:&space;\frac{18}{8}$  48 is divisible by 8, so we do not get a remainder and 18 when divided by 8, we get a remainder of 2.

Hence, 2 is the remainder.

Note : If you observe there is no use of the quotient here. We can directly work with the previous remainder. Which means.
Previous remainder is 3 and if the n is increased to 6n. Then 6 is multiplied with the previous remainder 3 = 18.
18 when divided by 8 leaves a remainder of 2. Hence 2, is the answer.

15. Alok deposits Rs.5,000 in his bank account for 5 years to earn an interest of 12%. What amount will he get after 5 years?
a. 2000          b. 3000          c. 8000          d. 8300
Solution: Given; Principle = 5000, time= 5 years and rate of interest = 12%
Amount = Simple interest + Principle
Simple Interest =  $\frac{P\,&space;*\,&space;t\,*\,&space;r}{100}$

Simple Interest = $\frac{5000\,&space;*\,&space;5\,&space;*\,&space;12}{100}$

Simple Interest = 3000
Amount = 3000 + 5000
Amount = 8000rs. Hence, he gets 8000 at the end of 5 years.

# Understanding Ratio and Proportions

## Type – 1 : Understanding ratio and proportions – The Basic Model

#### a. 35          b. 30          c. 89          d. 44

Solution : Now, this is one point I want you to understand in ratios and proportions. Whenever. you have ratios in the question, it helps us in eliminating certain choices. In this question he is asking for the number of men and we know men is representing the number 5. Hence, our answer should be divisible by 5. Out of all the choices 89 and 44 can be eliminated. This kind of an approach helps in solve problems with ease.

#### Step 1 :

Let us assume the ratio itself as the original value. Say, men are 5 and women are 7 in number. But, according to the question women are not 7, they are 42 in number. Now, increase your assumption to match the value given in the question.

#### Step 2 :

Increase your assumption by the same number. Hence, men are not 5 in number. Increasing your assumption by 6. They are 30 in number.

## Type – 2 : Addition, subtraction or multiplication of ratio

#### a. 210           b.195          c. 240          d. 65

Solution : Assuming the smallest number is 12 and the largest in 13. Because we are given the sum of the numbers in the question. We need to find the sum according to our assumption which is 25. Now, increase your assumption to match the value given in the question. Hence, the largest number we thought is 13 now, increasing the assumption by the same number 13 * 15 = 195.

#### a. 3000           b. 5000          c. 4000          d. 6000

Solution : We are being asked to find B’s salary. B is representing the number 3. Hence, our answer should be divisible by 3. With this Option B and C can be eliminated. Assuming the ratio itself as the original value, D gets 2 more than C.

Increase your assumption by 1000 to match the value given in the question. B is representing the number 3. Increase your assumption by the same number 1000. Hence, B gets 3000.

#### Solution : Method- 1

First of all, we are asked to find the largest number and from the ratio the largest value is 7. Therefore our answer should be divisible by 7. Out of all the choices only 84 is divisible by 7. Hence C is the right answer.

Otherwise; Let the first number be 7 and the second number be 6. Product according to our assumption is 42. But, according to the question its 6048. Now, dividing 6048 by 42 we get, 144. Unlike other questions we are suppose to take the square root of the increased assumption here (this can be better understood in method-2). Now, increase your assumption by the same number 12 with the largest number. Hence, 12 * 7 = 84.

### Method -2

This is the regular way of solving but, this method clearly shows why we need to take the square root of the increased assumption.

Let the numbers be 7x and 6x
7x * 6x = 6048
42x2 = 6048
x= 144
x = 12
Now larger number is 7x and x= 12 which is 7 * 12 = 84

#### A. 200             b. 400             c. 600              d. 640

Solution : First of all, lets focus on the underlined sentence.

Length is 50 meters more than the breadth means L= 40 + B

Consequently, L – B = 40 with this we can also understand that sentence as difference between length and the breadth is 40.

Now, assuming the ratio itself as the original value. Say, Length is 3 meters and Breadth is 2 meters. Difference between length and breadth according to my assumption is 1 meter. But, it is 40 according to the question. Increase your assumption by 40 to match the value in the question. Therefore, the original values of the length and breadth are 120 and 80 respectively.

Note : Perimeter of any figure means adding all the sides. As a result we need not know the formula in this case. Since it is a rectangle adding the length twice and the breadth twice gives us the perimeter.

#### a. 2500          b. 2400          c. 2600          d. 2700

Solution: Assuming the ratio itself as the original value again.

We know that :- Income – Expenditure = Savings

According to my assumption each person saves Rs 1. But, it is 600 in the question. Increasing my assumption by 600. As we are asked to find the income of A. Substituting 600 at the income of A. Therefore A’s income is 2400.

## Type – 3 : Combining the ratios

#### a. 4 : 5: 7           b. 4 : 3 : 7          c. 20 : 12 : 21           d. 21 : 12 : 20

Solution : Method – 1
The answer cannot be 4 : 3 : 7 or 4 : 5 : 7 because even if the variable B is common among bot the ratios since their associated numbers are not common we cannot combine the ratios. If the numbers were common we could have combined. So, our next step is to make the numbers common.

For which 3 is multiplied with 5 and 5 with 3. As, the second half of the ratio should also be multiplied with the same number 5 and 3 respectively. Now, the variable and the number is common. Hence, the combined ratio is 20 : 15 : 21.

Solution: Method – 2
Remember the shortcut as a pattern. Cross multiply the first two, the middle two and the last two. Make sure you are writing them in the same

#### Solution: We can apply the same shortcut pattern here as well. Do it for three variables first.

Now, include the fourth variable.

# Key for Week One document

## Ratio and Proportions

1. 40
2. 84
3. 195
4. 400
5. 600
6. 2000
7. 28
8. 2400
9. 20 : 12: 21
10. 15 : 20 : 8
11. 21 : 55
12. 4 : 12 : 30 : 45
13. 2400
14. 20097
15. 28
16. 60, 90, 360
17. 122
18. 21 : 22
19. 2 : 3 : 4
20. Cannot be determined
21. 810
22. 3125
23. 270
24. 320
25. 160
26. 2000
27. 60
28. 128
29. 100
30. 12

## Ages

1. 36
2. 72
3. 32
4. 9
5. 8
6. 32
7. 30
8. 28
9. 25
10. 55
11. 10
12. 3 : 4
13. 15
14. 20
15. 11 : 20 : 29
16. 28
17. 14
18. 13 : 22
19. 16
20. 40, 10
21. 62
22. 20
23. 93
24. 35
25. 27
26. 16
27. 60
28. 38
29. 3
30. 32, 23

## Percentages

1. 140
2. 4150
3. 9%
4. 500
5. 140
6. 2 : 3
7. 64%
8. 20%
9. 8% Increase
10. 0.8%
11. 4% Decrease
12. 25%
13. 20%
14. 78%
15. 10000
16. 10% decrease
17. 2.25% decrease
18. 1000
19. 68921
20. 57600
21. 120000
22. 10%
23. 2.1%
24. 20500
25. 19602
26. 120%
27. 75%
28. 20000
29. 18000
30. 35000
31. 200
32. 9000
33. 2000
34. 200
35. 300
36. 320
37. 980
38. 400
39. 42, 33
40. 62%
41. 400
42. 12
43. 4
44. 33 1/3 kg
45. 5 kg
46. 40
47. 3
48. 126
49. 12%

## Profit and Loss

1. 4%
2. 50%
3. 50%
4. 5%
5. 1260
6. 3%
7. 660
8. 200
9. 2500
10. 900
11. 400
12. 50
13. 25% Profit
14. 100/9 %
15. 20% Loss
16. 21%
17. 150%
18. 50%
19. 50%
20. 4000
21. 16
22. 40
23. 2000
24. 960
25. 11.11%
26. 25%
27. 23.25%
28. 5.55%
29. 360
30. 10000
31. 2040
32. Rs. 20
33. Cannot be determined
34. 37.5%
35. 33 1/3 %
36. 10%
37. 20%
38. 1% Loss
39. 400
40. 300
41. 500
42. 18000
43. 800
44. 9600
45. 80, 40
46. 7000, 5000
47. 44%
48. 34.09%
49. 32%

# Practice questions : Paper- I

1. If lion is called fish, fish is called parrot, parrot is called rat, rat is called cat, cat is called tiger, then which of the following is the bird?
a. fish          b. parrot          c. rat          d. tiger

Solution : From the entire list, Parrot is the bird. But, Parrot is called as rat. Hence rat is the right answer.

2. If Lilly is called lotus, lotus is called rose, rose is called sunflower and sunflower is called marigold, then what is the national flower of India?

Solution : The national flower of India is Lotus but, lotus is called as rose. Hence rose is the right answer.

3. On another planet, the local terminology for earth, water, light, air and sky are sky, light, air, water and earth respectively. If someone is thirsty there, what would he drink?

Solution : If someone is thirsty, we drink water. But, water is called as light on the other planet. Hence, Light is the correct answer.

4. If the animals which can walk are called swimmers animals who crawl are called flying, those living in water are called snakes and those which fly in the sky are called hunters, then what will a lizard be called?

Solution : Lizards crawl and animals who crawl are called flying. Hence Flying is the right answer.

5. In a certain language, ‘Sun shines brightly’ is written as ‘ba lo sul’, ‘houses are brightly lit’ as ‘kado ula ari ba’ and ‘light comes from sun’ as ‘dopi kup lo mo’. What are the code words for ‘Sun’ and ‘brightly’?

Solution : From the first two english sentences brightly is the common word. Then, the code used for brightly in the first sentence should be used in the second as well. Now, the coded word that is common among both the sentences is ba. Hence, brightly means ba.

Sun shines brightly ———- ba lo sul
houses are brightly lit———kado ula ari ba
light comes from sun———dopi kup lo mo

Hence, Brightly— ba   and   Sun — lo

6. In a certain code language ‘TRUE’ is coded as ‘USSQVTFD’ then what is the code for ‘PRAY’ ?
a. QSOQBZXZ          b. QOSQBZXZ          c. QOSQBZZX          d. QOSBQZZX

Solution : Pattern- Each letter is coded with its right and left letters respectively.

7.In a certain code ‘CLUB’ is coded as ‘XOFY’ and ‘NOT’ is coded as ‘MLG’, then how will ‘PUNCTUAL’ be coded as?

Solution : Pattern- Each letter of the word is coded with the opposite letter.

8. If ‘ORGANISATION’ is coded as ‘CBDWLQJWYQCL’ and ‘OPERATION’ is written as ‘CXFBWYQCL’. How is ‘SEPARATION’ coded as?

a. EJXEBYQCL          b. JFQYWBCXQL          c. JFXWBWYQCL          D. QCLYWBFXJE

Solution :

9. If ‘PERSON’ is coded as ‘STXWJU’ then how is ‘MOTHER’ coded as ?
a. RTYUJM          b. RTYJMU          c. WJMYTR          d. RTYMUJ

Solution : Pattern- Each letter of the word is coded as its next five letters.

(Question 10- 14) Seven persons A, B, C, D, E, F, G are sitting in a row in such a way that some are facing towards North and some are facing towards South. Not more than two consecutive persons face same direction. A sit at one of the ends and faces North direction. The number of persons sitting between A and G is same as between G and B. E sits on to the immediate right of C. G sits to the right of A but not immediate right. B faces same direction as A and C. Three persons sit between F and A. F and D face same direction.

Solution :

Step-1 : From  ” A sit at one of the ends and faces North direction” and “G sits to the right of A but not immediate right” says that A is onto the extreme left

Step-2 : According to this “Three persons sit between F and A”(given in the question)

Step -3 : As the question has The number of persons sitting between A and G is same as between G and B”. To satisfy this G has to be at the center of the row and with equal distance we can place B.

Step- 4: As “E sits on to the immediate right of C” is given in the info, there are only two consecutive places to place C and E next to each other.

Step-5 :  As only one blank and one person is left out. D comes there.

Step- 6: According to this — B faces same direction as A and C”

Step -7 : According to this — Not more than two consecutive persons face same direction”. As A and C are facing North E should be facing South. Also it given that “F and D face same direction”, they cannot be facing North because then it violates the condition in the question. Hence, F and D are facing South.

Step-8 : Again, according to the previous condition G cannot be facing South as Not more than two consecutive persons face same direction”. Hence G is facing North.

10. How many persons are facing north?
a. more than 3          b. three             c. none                  d. two             e. one

Solution : More than 3 [ A, C, G, B]

11. Which of the following pair represents the persons sitting at the ends?
a. D-E          b. A-B          c. F-C          d. G-B          e. A-C

Solution : A-B are at the ends of the row

12. Four of the following five form a group, which of them does not belong to the group?
a. C          b. A          c. B          d. G          e. E

Solution : E, because only E from the list faces South.

13. Who among the following sits third to the left of F?
a. C          b. A          c. B          d. G          e. No one

Solution : No one.

14. Who sits to the immediate right of A?
a. C         b. D           c. B          d. G          e. E

Solution: C is onto the immediate right of A.

Six couples have been invited to a dinner party. They are Neetu, Misha, Lilly, Ramya, Shanti, Charitha and Farookh, Himesh, Ajit, Tarun, Ram, Arun. They are seated on a circular table facing each other.
(i) Misha refuses to sit next to Arun.
(ii) Lilly wants to be between Ajit and Himesh.
(iii) Charitha refuses to sit next to Farookh.
(iv) Neetu is seated on Arun’s right hand side.
(v) Farookh and Tarun are seated exactly opposite to each other.
(vi) Ram and Shanti are seated to the left of Charitha.
(vii) Ajit and Ramya want to enjoy the company of Lilly and Tarun respectively and are seated closest to them.
(viii) The seating arrangement is such that minimum one woman is always between two men.

Solution : Step-1 : Because of last condition (The seating arrangement is such that minimum one woman is always between two men). The template of the arrangement looks like this.

Step-2 : According to this condition — “Lilly wants to be between Ajit and Himesh.”

Step-3 : According to this condition — “Ajit and Ramya want to enjoy the company of Lilly and Tarun respectively and are seated closest to them.”

Step-4 : According to this — “Farookh and Tarun are seated exactly opposite to each other.”

Step-5 : As “Charitha refuses to sit next to Farooq”

Step-6 : According to this condition — Ram and Shanti are seated to the left of Charitha”. We can position Charitha’s place. With that Ram and Shanti’s place can also be positioned

Step-7 : To satisfy this condition — “Neetu is seated on Arun’s right hand side”. With the only two consecutive places we can place Neetu and Arun

Step-8 : Hence, only one blank and one person is left out. Misha can be placed there.

15. Which of the following statements is correct:
a. Lilly is on Tarun’s right     b. Arun is on Charitha’s right
c. Misha is on Himesh’s right     d. Misha is on Farookh’s left

Solution : Clearly, Arun is onto Charitha’s right.

16. If looked in an anti-clockwise manner, who are seated between Tarun and Farookh:
a. Shanti, Ram, Charitha, Arun and Neetu       b. Shanti, Ram, Ramya, Ajit and Lilly
c. Shanti, Ram, Misha, Himesh and Lilly          d. Shanti, Ram, Lilly, Ajit and Himesh

Solution : Anti-clockwise is from Tarun’s right — Shanti, Ram, Charitha, Arun and Neetu are between Tarun anf Farooq.

17. Which of the following close neighboring arrangements is correct:
a. Arun, Charitha and Ram          b. Tarun, Ram and Arun
c. Neetu, Farookh and Lilly         d. Himesh, Misha and Ajit

Solution : Close neighborsArun, Charitha and Ram from the choices

Eight friends A, B, C, D, E, F, G and H are sitting in a circle. D is between B and G and F is between A and H. E is second to the right of A.

Solution :
Step-1 : From “D is between B and G”. We cannot say if B will be on to the right or left of D.

Step-2 : According to these two conditions —F is between A and H, E is second to the right of A.”

Step -3 : Only one blank and one person is left out. Hence, C comes here.

18. Which of the following is A’s position?
a. left of F         b. right of F         c between E and F          d. cannot be determined

Solution : From the diagram, A is to the right of F.

19. Which of the following information is not required to ascertain the position of c?
a. I           b.either II or III            c. III                 d. All required

Solution : We need all the information to place C.

# Partnership – Basic Models

## Model 1: Distribution of Profit

1.Meena started a business investing 12000. After 5 months, Abhay joined her with a capital of 9000. At the end of the year, the total profit was 4416. What is the share of profit of Meena?
a. 1344          b. 3364          c. 3072          d. 2568          e. None of these

Solution : As Meena started the business her investment will be there for 12 months and as Abhay joined after 5 months, his investement will be there for 7 months(12-5).

2. Tanvi started a business investing 45,000. After 8 months Anisha joined her with a capital of 52,000. At the end of the year, the total profit was 56,165. What is the share of the profit of Anisha?
a. 21450          b. 24440          c. 27635          d. 317650          e. None of these

Solution : As Tanvi started the business her investment will be there for 12 months and as Anisha joined after 8 months, his investement will be there for 4 months(12-8).

56165 is not divisible by 187. You can round off the value to 300. Hence, none of these is the right answer.

3. P, Q and R invested 45,000, 70,000 and 90,000 respectively to start a business. At the end of two years, they earned a profit of 1, 64,000. What will be Q’s share in the profit?
a. 56,000          b. 35,000          c. 72,000          d. 64,000          e. None of these

Solution : They all invested for the same period of time(2 years)

4. Prakash, Sunil and Anil started a business jointly investing 11 lakhs, 16.5 lakhs and 8.25 lakhs respectively. The profit earned by them in the business at the end of three years was 19.5 lakhs. What will be the 50% of Anil’s share in the profit?
a. 4.5 lakhs          b. 2.25 lakhs          c. 2.5 lakhs          d. 3.75 lakhs          e. None

Solution : They all invested for the same period of time(3 years)

5. A, Band C enter into a partnership. A contributes 320 for 4 months, B contributes 510 for 3 months and C contribute 270 for 5 months. If the total profit is 208, what will be the share of A?
a. 92          b.  64          c. 88          d. 94           e. 56

Solution : In this question the time period for every individual is different.

6. Pankaj and Nitin started a business investing 42,000 and 57,000 respectively, but Nitin left the business after 8 months. Find the difference between the share of profits of Pankaj and Nitin, if the total profit at the end of the year was 26,000?
a. 1200          b. 1400          c. 1600          d. 1300            e. None of these

Solution : As Pankaj started the business his investment will be there for 12 months and Nithins left after 8 months means that out of 12 months he was there only for 8 months

7. Prabha started a business investing 32000. After 5 months, Amit joined her with a capital of 22,000. At the end of the year, the total profit was 16,409. What is the difference between the shares of Prabha and Amit?
a. 5,284          b. 11,712          c. 10,182          d. 7015          e. None of these

Solution : Amit joined after 5 months which means out of 12 months he was not there in the business for 5 months. Hence, his investment was there only for 7 months.

8.Arun started a business investing 38,000. After 5 months Bakul joined him with a capital of 55,000. At the end of the year, the total profit was 22,000. What is the approximate difference between the share of profit of Arun and Bakul?
a. 1192          b. 1856          c. 1007          d. 1928          e. 1568

Solution : Bakul joined after 5 months. Hence, out of 12 months he was not there for 5 months therefore his investment is there for 7 months.

9. Sarita started a business investing 50000. After six months, Abhishek joined her with 75000. After another six months, Nisha also joined them with 1.25 lakh. What should be the ratio in which the profits are shared by the 3 persons respectively at the end of 2 years?
a. 4:5:6          b. 8:9:10          c. 8:9:12           d. 4:5:8          e. None of these

Solution : Abhishek joined after 6 months. Hence, Out of 24 months ( 2 years) he was there only for 18 months and Nisha joined after another six. Another 6 means in continuation with the previous statement, therefore she was not there for 12 months. Out of 24 months, she was there for 12 months.

## Model 4: Additional Investments after a Certain Period

10. Subhash started a business by investing 25,000. 6 months later Aditya joins him by investing 15,000. After another 6 months. Aditya invests an additional amount of  15,000. At the end of 3 years they earn a profit of 2, 47,000. What is the Aditya’s share in the profit?

a. 1,13,000          b. 1,23,000           c. 1,17,000          d. 1,11,500           e. None of these

Solution : Unlike the previous questions, here the investor makes changes with the initial investment. Aditya joins after 6 months means out of 36 months( given) he was not there for 6 months. After another 6 months he adds 15000 more. Now, his investment of initial 15000 was undisturbed for 6 months and a sum of 30000 altogether was there for 24 months.

# Previous Gate Questions

1. Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability that only one of them is selected ? (Gate -2015)

a. 47/48          b. 1/4          c. 13/48          d. 35/48

Here, we want the probability of anyone of them being selected.

Which means either ‘Ram is selected and Ramesh is not selected’ or ‘ Ramesh is selected and Ram is not selected’.

The probability of Ram or Ramesh not getting selected is [1 — selection probability].

‘Ram is selected and Ramesh is not selected’ or ‘ Ramesh is selected and Ram is not selected’.

Option B is the right answer

# The power of even and odd

### Example :

There are two, 2- digit numbers ab and cd, ba is another 2- digit number prepared by reversing the digits of ab, if ab * cd = 493 and ba * cd = 2059. What is the value of (ab + cd)?

A. 43          B. 45          C. 47          D. 46