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CASLET DI

Directions :- Study the following data carefully and answer the questions given below it .

The total number of students in a institute having three disciplines viz. Arts, Commerce and Science is 19,000. 25% of the total numbers of students are from the discipline of Arts. 35% of the total numbers of students are from the discipline of Commerce and 40% of the total numbers of students are from the discipline of Science. The institute has three compulsory subjects viz. Social Work, Physical Training and Cookery for all the three disciplines and the students have a choice to take either one of the subjects or all the three subjects together. 24% of the total numbers of students from the discipline of Arts have taken Social Work. 30% of the total numbers of students from the discipline of Arts have taken Physical Training. 40% of the total numbers of students from the same discipline have taken Cookery and the rest have taken all the three subjects. 44% of the total numbers of students from the discipline of Commerce have taken Social Work, 28% have taken Physical Training, 14% have taken Cookery and the rest have taken all the three subjects. 35% of the total numbers of students from the discipline of Science have taken Social Work, 43% have taken Physical Training, 4% have taken Cookery and the rest have taken all the three subjects.

1. The total numbers of students who have taken all the three subjects are what per cent of the total number of students in the institute?

A15
B12.5    
C13.6 
D14.8  
ENone of these

2.What is the total number of students in the institute who have taken only Cookery as their subject?

A3180
B3200
C3020
D3135
ENone of these

3.The total numbers of students who have taken only Social Work as their subject from the discipline of Arts are approximately what per cent of the total number of students taking the same subject from the discipline of Science?

A43
B48
C36
D28
E51

4.What is the total number of students who have taken Social Work and Physical Training from all the three disciplines?

A13855
B9861
C10281
D12555
ENone of the above

5.What is the respective ratio of the total number of students from the discipline of Commerce to those from the discipline of Science?

A9:8  
B7:8    
C8:9  
D8:7  
ENone of these

DIRECTION ( 6 - 10 )

There are three companies A, B, and C. The employees of the company can speak at least one of three languages Hindi, English, and Spanish in the following manner.

In company A, 700 employees speak Hindi, 600 speak English, and 555 Spanish. In company B, 650 speak Hindi, 580 speak English, and 700 speak Spanish. And in company C, 500 speak Hindi, 600 English, and 700 Spanish.

The number of employees of company A who speak only Hindi is equal to that of company C who speak English and Spanish but not Hindi. It is also equal to that of company B who speaks all the three languages.

The number of employees of company C who speak only Spanish is equal to 180 which is 20% more than the number of employees of company B who speak only Hindi.

The ratio of the number of employees of company C who speak only English to the number of employees of company A who speak only Spanish to the number of employees of company B who speaks only Hindi is 2:4:5.

The number of employees of company A who speak only English is equal to the number of employees of company B who speak only Spanish, which is equal to 180, which is also 25% less than those who speak English and French but not Hindi in company C.

The number of employees of company C who speak Hindi and Spanish but not English is equal to the number of employees of company A who speak English and Hindi but not Spanish, which is equal to the number of employees of company B who speak English and Spanish but not Hindi.

The number of employees of company A who speak Spanish and Hindi but not English is 165, which is 10% more than those who speak Hindi and Spanish but not English in company C.

Q6. How many employees Hindi and English but not Spanish on company C?

1) 130

2) 80

3) 150

4) 170

5) none of these.

Q7-. How many employees can speak all three languages in company A?

1) 145

2) 125

3) 130

4) 150

5) None of these

Q8-. How many employees speak any two of the three languages in company B?

1) 540

2) 410

3) 670

4) cannot be determined

5) None of these

Q9-. The number of employees of company A who speak English and Spanish but not Hindi is what percent more than the number of those who speak only Hindi in company C?

1) 125%

2) 60%

3) 150%

4) 100%

5) None of these

Q10. What is the difference between the number of employees of company C who speak all the three languages and the number of employees of company B who speak only English?

1) 10

2) 20

3) 50

4) 110

5) none of these.

Direction ( 11 - 15 )

The table shows the number of students participated in different sections from different schools.

11) A group of four students has to form from school C such that the group contains one student in each section and the remaining from any of the section. The number of ways in which this can be possible is 25920. Find the number of students in section III from school C?

a) 15

b) 12

c) 10

d) 20

e) 18

12) A group of two students has to form from school E such that the group contains at least one student in section III. The number of ways in which this can be possible is 195. A committee of five students is to be formed from school E such that the committee contains 2 students from section I, 1 student from section II and 2 students from section III. Find the number of ways in which this can be possible?

a) 15920

b) 16478

c) 23420

d) 17820

e) None of these

13) Find the total number of students in school A?

Statement I: All the students in section II from school A is handshaking with each other and the total number of handshakes is 105.

Statement II: All the students in school A is handshaking with each other and the total number of handshakes is 780.

a) Only I

b) Only II

c) Both I and II

d) Either I or II

e) Neither I nor II

14) In school B, number of students in section III is 75% of the number of students in section II.

Quantity I: In committee P, five students is to be formed from school B such that the committee contains 1 student from each section and the remaining students from any of the section.

Quantity II: In committee Q, five students is to be formed from school B such that committee contains at least one student from section I.

a) Quantity I > Quantity II

b) Quantity I < Quantity II

c) Quantity I ≥ Quantity II

d) Quantity I ≤ Quantity II

e) Quantity I = Quantity II (or) Relationship cannot be determined

15) A committee of three members is to be formed from each school B and school D. Number of possible ways of a committee contains three students in section III from school D is what percentage of the number of possible ways of committee contains three students in section I from school B? 

a) 180%

b) 380%

c) 160%

d) 280%

e) None of these

Directions (16 – 20): Study the following information carefully and answer the given questions

Three bags A, B and C contains three different coloured balls Red, Blue and Yellow.

Bar graph given below shows the number of Red colour balls in three different bags A, B and C while the pie chart given below shows the distribution (degree) of Blue colour balls in those three bags.


Some extra information is also given:

When two balls are selected at random from bag A, then probability that one of them is Red and other is Blue is (20/119) and ratio of Blue to Yellow balls in that bag is 3: 5.

When two balls are selected at random from bag B, then probability that both the balls are Blue is (49/447). The difference between the probability of selecting a Blue ball from bag C and the probability of selecting Blue ball from bag B is 1/4.

16) If two balls from bag A, one ball from bag B and one ball from bag C, then what is the probability that both the balls selected from bag A is of Red colour,ball selected from bag B is of Yellow colour and ball selected from bag C is of Blue colour?

a) (8/365)

b) (13/765)

c) (3/65)

d) (10/67)

e) None of these

17) What is the difference between the probability of selecting two Bluecolour balls from bag A and the probability of selecting either ared colour ball or a blue colour ball from bag B?

a) (401/7140)

b) (481/7400)

c) (5903/7400)

d) (4801/7140)

e) None of these

18) The difference between the probabilities of selecting one blue colour ball from bag A and bag B is approximately how much per cent less than the difference between the probabilities of selecting one red colour ball from bag B and bag C?

a) (450/7)%

b) (550/9)%

c) (250/3)%

d) (350/9)%

e) None of these

19) If twoballsare selected at random from each of the bag B and bag C, then what is the probability the both the selected balls are one among the red colour or of blue colour or of yellow colour?

a) (9/16)

b) (93/180)

c) (17/36)

d) (11/36)

e) None of these

20) If ‘p’ number of yellow colour balls from bag C are transferred to bag B and 83(1/3)% of total red colour balls from bag B are transferred to bag C, then the probability of selecting either a red colour ball from bag Bor a blue colour ball from bag C is (11/20), then what is the value of ‘p’.

a) 25

b) 20

c) 10

d) 15

e) None of these

SOLUTIONS:

(1 - 5) 

1.The percentage of total number of students who have taken all the three subjects to the total number of students in the institute= (2584/19000) × 100=13.6

2.∴The total no. of students in the institute who have taken only Cookery as their subject
= 1900 + 931 + 304
= 3135

3.The percentage of the total no. of students from the discipline of Arts who took Social Work to the total no. of students taking the same subject from the discipline of Science
= (1140/2660) ×100
= 42.857
≈ 43 

4.∴The total number of students who have taken Social Work and Physical Training from all the three disciplines = 1140 + 1425 + 2926 + 1862 + 2660 + 3268
= 13281 

5.The ratio of the total number of students from the discipline of Commerce to those from of Science= [19000 × (35/100)] : [19000 × (40/100)]
= 35 : 40
= 7 : 8

Solutions—




 Number of employees of company C who speak all the three languages= 700-(180+240+150) = 130

Now the number of employees of company C who speak Hindi and English but not Spanish= 600- (240+130+60) = 170

Number of employees of company B who speak Hindi and English but not Spanish= 580- (60+150+240) = 130
Number of employees of company B who speak Hindi and Spanish but not English= 700-(180+150+240)= 130

Total number of employees of company B any two of three languages = 130+130+150 = 410.

Number of employees of company A who speak English and Spanish but not Hindi= 125
Number of employees of company C who speak only Hindi = 50

Required % = 125-50/50*100

= 150%

Required difference= 130-60 = 70
 
Number of employees in company B= 700+60+130+150= 1040
Number of employees in company C = 700+60+170+50= 980

Required% = 1040-980/980*100

~6%

Directions (11-15) :

11) Answer: c)

No of students in section III from school C = x

Total number of students in school C = x + 8 + 12 = 20 + x

Number of possible ways = 8C1 * 12C1 * xC1 * (20 + x – 3) C1 = 25920

8 * 12 * x * (17+x) = 25920

17x + x2 = 270

= > x2 + 17x – 270 = 0

= > x2 – 10x + 27x – 270 = 0

= > x (x – 10) + 27 (x – 10) = 0

= > x = 10, – 27 (Eliminate the –Ve value)

Number of students in section III from school C = 10

12) Answer: d)

Number of students in section III from school E = y

Total number of students in school E = (y + 12 + 18)

= y + 30

Number of possible ways = yC1 * 30C1 + yC2 = 195

= > y * 30 + (y*(y-1)/(1 *2)) = 195

= > 30y + (y2 – y)/2 = 195

= > 60y + y2 – y = 390

= > y2 + 59y – 390 = 0

= > y2 + 65y – 6y – 390 = 0

= > y (y + 65) – 6 (y + 65) = 0

= > (y + 65) (y – 6) = 0

= > y = 6, -65 (Eliminate –Ve value)

Total number of students in school E = 30 + 6 = 36

Required number of ways = 12C2 * 18C1 * 6C2

= (12*11 / 1*2) *18 *(6*5 / 1*2)

= 6*11*18*3*5

= 17820

13) Answer: b)

From I,

Number of students in section II from school A = n

Number of handshakes = nC2 = 105

> [n*(n -1)] / (1 * 2) = 105

= > n2 – n = 210

= > n2 – n – 210 = 0

= > n2 – 15n + 14n – 210 = 0

= > (n – 15) (n – 14) = 0

= > n = 15, -14 (Eliminate –Ve value)

From statement I, We have to find only number of students in section II from school A. We can’t find the total number of students.

Hence, statement I alone is not sufficient to answer the given question.

From II,

Total number of students in school A = x

Number of handshakes = xC2 = 780

= > x * (x – 1)/1*2 = 780

= > x2 – x = 780*2

= > x2 – x – 1560 = 0

= > x2 – 40x + 39x – 1560 = 0

= > x (x – 40) + 39 (x – 40) = 0

= > (x – 40) (x + 39) = 0

= > x = 40, -39 (Eliminate –Ve value)

Total number of students in school A is 40.

Hence, Statement II alone is sufficient to answer the given question.

14) Answer: a)

Number of students in section II from school B = x

Number of students in section III from school B = 75/100 * x

= 3x/4

Total number of students in section II and III from school B = 20 – 6 = 14

= > x + 3x/4 = 14

= > 7x/4 = 14

= > x = 8

Number of students in section III from school B = 8 * 75/100 = 6

Quantity I:

Number of ways = 6C1*8C1*6C1*(20-3)C2

= 6 * 8 * 6 *(17*16/1*2)

= 6*8*6*17*8

= 39168

Quantity II: In committee Q, five students is to be formed from school B such that committee contains at least one student from section I.

Number of ways = 6C1*14C4 + 6C2*14C3 + 6C3*14C2 + 6C4*14C1 + 6C5

= 6006 + 5460 + 1820 + 210 + 6

= 13502

Hence, Quantity I > Quantity II

15) Answer:  d)

Number of ways in school D = 8C3

= 8*7*6 / 1*2*3 = 56

Number of ways in school B = 6C3

= 6*5*4 / 1*2*3 = 20

Required percentage = (56/20) * 100 = 280%

Directions (16 – 20):

Ratio of number of Blue colour balls in bag A, B and C = 72: 120: 168 = 3: 5: 7

Let number of blue balls in bag A, B and C is 3x, 5x and 7x respectively.

Number of yellow balls in bag A = 3x * (5/3) = 5x

Total balls in bag A = (40 + 3x + 5x) = (40 + 8x)

Probability when two balls are selected from bag A and out of which one Red and other is Blue = [(40C1 * 3xC1)/(40 + 8x)C2] = 20/119

120x/(20 + 4x)(39 + 8x) = 20/119

3x/(5 + x)(39 + 8x) = 2/119

357x = 16x2 + 158x + 390

16x2 – 199x + 390 = 0

16x2 – 160x – 39x + 390 = 0

16x (x – 10) – 39 (x – 10) = 0

(16x – 39) (x – 10) = 0

= > x = 10, 39/16 (Eliminate the fraction value)

x = 10

Number of Blue balls in bag A = 3x = 30

Number of Yellow balls in bag A = 5x = 50

Total balls in bag A = 40 + 30 + 50 = 120

Number of Blue balls in bag B = 5x = 50

Number of Blue balls in bag C = 7x = 70

Let the number of yellow balls in bag B = b

Total balls in bag B = (60 + 50 + b) = (110 + b)

Probability when two Blue balls are selected from bag B = 50C2/(110 + b)C2

= (49/447)

(50 * 49)/[(110 + b)(110 + b – 1)] = 49/447

50/[(110 + b) (109 + b)] = 1/447

22350 = 11990 + 110b + 109b + b2

22350 = 11990 + 219b + b2

b2 + 219b – 10360 = 0

b2 + 259b – 40b – 10360 = 0

(b + 259) (b – 40) = 0

= > b = 40, -259 (Eliminate –ve value)

b = 40

Number of yellow balls in bag B = b = 40

Total balls in bag B = 60 + 50 + 40 = 150

Let the number of yellow balls in bag C = c

Probability of selecting a Blue ball from bag B = 50/150 = 1/3

Total balls in bag C = (20 + 70 + c) = (90 + c)

Probability of selecting a Blue ball from bag C = 70/(90 + c)

According to the question:

[70/(90 + c)] – (1/3) = 1/4

70/(90 + c) = 7/12

10/(90 + c) = 1/12

120 = 90 + c

c = 30

Number of yellow balls in bag C = c = 30

Total balls in bag C = 20 + 70 + 30 = 120

16) Answer: b)

Probability of selecting two red balls from bag A = 40C2/120C2

= (20 * 39)/(60/119) = (13/119)

Probability of selecting one yellow ball from bag B = 40/150 = (4/15)

Probability of selecting one blue ball from bag C = 70/120 = (7/12)

Required probability = (13/119) * (4/15) * (7/12) = (13/765)

17) Answer: d)

Probability of selecting two Blue colour balls from bag A = 30C2/120C2 = (29/476)

Probability of selecting either a red colour ball or a blue colour ball from bag B

= (60/150) + (50/150) = (11/15)

Required difference = (11/15) – (29/476) = (5236 – 435)/7140

= (4801/7140)

18) Answer: a)

Probability of selecting one blue colour ball from bag A = (30/120) = (1/4)

Probability of selecting one blue colour ball from bag B = (50/150) = (1/3)

Difference = (1/3) – (1/4) = (1/12)

Probability of selecting one red colour ball from bag B = (60/150) = (2/5)

Probability of selecting one red colour ball from bag C = (20/120) = (1/6)

Difference = (2/5) – (1/6) = (7/30)

Required per cent = [{(7/30) – (1/12)}/(7/30)] * 100 = (450/7)%

19) Answer: e)

Probability that both the selected balls from bag B and C are of red colour

= (60/150) * (20/120) = (1/15)

Probability that both the selected balls from bag B and C are of blue colour

= (50/150) * (70/120) = (7/36)

Probability that both the selected balls from bag B and C are of yellow colour

= (40/150) * (30/120) = (1/15)

Total probability = (1/15) + (7/36) + (1/15) = (59/180)

20) Answer: b)

After transfer, number of red colour balls in bag B = 60 – [83(1/3)% of 60]

= 10

After transfer, number of yellow colour balls in bag B = (40 + p)

Total balls in bag B after transfer = 10 + 50 + (40 + p) = (100 + p)

After transfer, number of red colour balls in bag C = 20 + [83(1/3)% of 60]

= 70

After transfer, number of yellow colour balls in bag C = (30 – p)

Total balls in bag C after transfer = 70 + 70 + (30 – p) = (170 – p)

Probability of selecting a red colour ball from bag B = [10/(100 + p)]

Probability of selecting a blue colour ball from bag C = [70/(170 – p)]

According to the question:

[10/(100 + p)] + [70/(170 – p)] = (11/20)

20[10(170 – p) + 70(100 + p)] = 11(100 + p)(170 – p)

20[1700 – 10p + 7000 + 70p) = 11(17000 + 70p – p2)

174000 + 1200p = 187000 + 770p – 11p2

11p2 + 430p – 13000 = 0

11p2 – 220p + 650p – 13000 = 0

11p (p – 20) + 650 (p – 20) = 0

= > p = 20, – 650/11 (Eliminate –ve value)

p = 20


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