AAO Exam-CT 13: Quant (DI - Caselet)

AAO Exam-CT 13- Quant (DI - Caselet)

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AAO Exam-CT 13: Quant (DI - Caselet)

1. Direction : Study the below data carefully and answer accordingly.

There are 4000 players in a sports academy. They are playing in three sports namely, Cricket, Football, and Hockey. The Ratio of male to female players is 11 ∶ 9. 40% of the players are playing cricket.  Men playing football are 25% of total male players. The numbers of female players in football are half the number of players in cricket. The ratio of male and female players in hockey is 4 ∶ 3.

Question:

What percent male players playing cricket from the total number of male players?

  • 37.35%
  • 27.25%
  • 40%
  • 47.72%
  • 20%

Shortcut Trick

Sports Male Female  
Cricket     40% of total players
Football   20% of total players 25% of 11x
Hockey 4y 3y  
  11x 9x  
       
Sports Male Female  
Cricket 1050 550 1600
Football 550 800 1350
Hockey 600 450 1050
  2200 1800 4000

Alternate Method

Given:

Total players = 4000

Ratio of male and female players = 11 ∶ 9

Total number of players in cricket = 40% of the total players

Male players in football = 25% of total male players

Female players in football = (1/2) of the players in cricket

The ratio of male and female players in hockey = 4 ∶ 3

Calculation:

Let the male and female players be 11x and 9x respectively

Now,

11x + 9x = 4000

⇒ 20x = 4000

⇒ x = 200

Number of male players = 11 × 200

⇒ 2200

Total number of Players in cricket = 40% of 4000

⇒ (40/100) × 4000

⇒ 40 × 40

⇒ 1600

Now,

Female players in football = (1/2) × 1600

⇒ 800

Now,

Male players in football = 25% of 2200

⇒ (25/100) × 2200

⇒ 25 × 22

⇒ 550

Now,

Total number of players in football = (800 + 550)

⇒ 1350

Now,

Total number of Players in hockey = 4000 – (Total number of Players in cricket + Total number of players in football)

⇒ 4000 – (1600 + 1350)

⇒ 4000 – 2950

⇒ 1050

Now,

Let the male and female players in hockey be 4x and 3x respectively

Now,

4x + 3x = 1050

⇒ 7x = 1050

⇒ x = 1050/7

⇒ x = 150

Now,

Number of male players in hockey = 4x

⇒ 4 × 150

⇒ 600

Now,

Total male players in cricket = 2200 – (Male players in football – Male players in hockey)

⇒ 2200 – (550 + 600)

⇒ 2200 – 1150

⇒ 1050

Now,

Required percent = (1050 /2200) × 100

⇒ 1050/22

⇒ 47.72

 Male players in the cricket will be 47.72%

2. Direction : Study the below data carefully and answer accordingly.

There are 4000 players in a sports academy. They are playing in three sports namely, Cricket, Football, and Hockey. The Ratio of male to female players is 11 ∶ 9. 40% of the players are playing cricket.  Men playing football are 25% of total male players. The numbers of female players in football are half the number of players in cricket. The ratio of male and female players in hockey is 4 ∶ 3.

Question:

What is the ratio of female players in football to the female players in hockey?

  • 7 : 9
  • 9 : 7
  • 9 : 16
  • 16 : 9
  • None of these

Shortcut Trick

Sports Male Female  
Cricket     40% of total players
Football   20% of total players 25% of 11x
Hockey 4y 3y  
  11x 9x  
       
Sports Male Female  
Cricket 1050 550 1600
Football 550 800 1350
Hockey 600 450 1050
  2200 1800 4000

Alternate Method

Given:

Total players = 4000

Ratio of male and female players = 11 ∶ 9

Total number of players in cricket = 40% of the total players

Male players in football = 25% of total male players

Female players in football = (1/2) of the players in cricket

The ratio of male and female players in hockey = 4 ∶ 3

Calculation:

Let the male and female players be 11x and 9x respectively

Now,

11x + 9x = 4000

⇒ 20x = 4000

⇒ x = 200

Number of male players = 11 × 200

⇒ 2200

Total number of Players in cricket = 40% of 4000

⇒ (40/100) × 4000

⇒ 40 × 40

⇒ 1600

Now,

Female players in football = (1/2) × 1600

⇒ 800

Now,

Male players in football = 25% of 2200

⇒ (25/100) × 2200

⇒ 25 × 22

⇒ 550

Now,

Total number of players in football = (800 + 550)

⇒ 1350

Now,

Total number of Players in hockey = 4000 – (Total number of Players in cricket + Total number of players in football)

⇒ 4000 – (1600 + 1350)

⇒ 4000 – 2950

⇒ 1050

Now,

Let the male and female players in hockey be 4x and 3x respectively

Now,

4x + 3x = 1050

⇒ 7x = 1050

⇒ x = 1050/7

⇒ x = 150

Now,

Number of male players in hockey = 4x

⇒ 4 × 150

⇒ 600

Number of female players in hockey = 3x

⇒ 3 × 150

⇒ 450

Now,

Required ratio = 800 ∶ 450

⇒ 80 ∶ 45

⇒ 16 ∶ 9

 The Ratio of female players in football to the female players in hockey will be 16  9

3. Direction : Study the below data carefully and answer accordingly.

There are 4000 players in a sports academy. They are playing in three sports namely, Cricket, Football, and Hockey. The Ratio of male to female players is 11 ∶ 9. 40% of the players are playing cricket.  Men playing football are 25% of total male players. The numbers of female players in football are half the number of players in cricket. The ratio of male and female players in hockey is 4 ∶ 3.

Question:

What is the difference between the number of male players in hockey and football?

  • 55
  • 45
  • 60
  • 50
  • None of these

Shortcut Trick

Sports Male Female  
Cricket     40% of total players
Football   20% of total players 25% of 11x
Hockey 4y 3y  
  11x 9x  
       
Sports Male Female  
Cricket 1050 550 1600
Football 550 800 1350
Hockey 600 450 1050
  2200 1800 4000

Alternate Method

Given:      

Total players = 4000

Ratio of male and female players = 11 ∶ 9

Total number of players in cricket = 40% of the total players

Male players in football = 25% of total male players

Female players in football = (1/2) of the players in cricket

The ratio of male and female players in hockey = 4 ∶ 3

Calculation:

Let the male and female players be 11x and 9x respectively

Now,

11x + 9x = 4000

⇒ 20x = 4000

⇒ x = 200

Number of male players = 11 × 200

⇒ 2200

Total number of Players in cricket = 40% of 4000

⇒ (40/100) × 4000

⇒ 40 × 40

⇒ 1600

Now,

Female players in football = (1/2) × 1600

⇒ 800

Now,

Male players in football = 25% of 2200

⇒ (25/100) × 2200

⇒ 25 × 22

⇒ 550

Now,

Total number of players in football = (800 + 550)

⇒ 1350

Now,

Total number of Players in hockey = 4000 – (Total number of Players in cricket + Total number of players in football)

⇒ 4000 – (1600 + 1350)

⇒ 4000 – 2950

⇒ 1050

Now,

Let the male and female players in hockey be 4x and 3x respectively

Now,

4x + 3x = 1050

⇒ 7x = 1050

⇒ x = 1050/7

⇒ x = 150

Now,

Number of male players in hockey = 4x

⇒ 4 × 150

⇒ 600

Number of female players in hockey = 3x

⇒ 3 × 150

⇒ 450

Now,

Required difference = (600 – 550)

⇒ 50

 The difference between the number of male players in hockey and football will be 50 players.

4. Direction : Study the below data carefully and answer accordingly.

There are 4000 players in a sports academy. They are playing in three sports namely, Cricket, Football, and Hockey. The Ratio of male to female players is 11 ∶ 9. 40% of the players are playing cricket.  Men playing football are 25% of total male players. The numbers of female players in football are half the number of players in cricket. The ratio of male and female players in hockey is 4 ∶ 3.

Question:

What is the number of female players in football?

  • 700
  • 750
  • 850
  • 800
  • None of these

Given:

Total players = 4000

Ratio of male and female players = 11 ∶ 9

Total number of players in cricket = 40% of the total players

Female players in football = (1/2) of the players in cricket

Calculation:

Players in cricket = 40% of 4000

⇒ (40/100) × 4000

⇒ 40 × 40

⇒ 1600

Now,

Female players in football = (1/2) × 1600

⇒ 800

 The Number of females players in the football will be 800

Alternate Method

Sports Male Female  
Cricket     40% of total players
Football   20% of total players 25% of 11x
Hockey 4y 3y  
  11x 9x  
       
Sports Male Female  
Cricket 1050 550 1600
Football 550 800 1350
Hockey 600 450 1050
  2200 1800 4000

5. Direction: Go through the passage given below and answer the question based on it.

There are four streams offered by a college viz. science, arts, agriculture, and commerce. 22.5% of total students are enrolled in the agriculture stream and there are 1000 students enrolled in the arts stream. The Commerce stream has 1200 students which are 15% of total students in the college.

Question:
how much percent more student is in the science stream than the number of students in the arts and commerce stream together?
  • 81" role="presentation" style="box-sizing: border-box; display: inline; font-style: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; user-select: initial !important;" tabindex="0">911911%
  • 11" role="presentation" style="box-sizing: border-box; user-select: initial !important; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">111111%
  • 83" role="presentation" style="box-sizing: border-box; user-select: initial !important; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">1919%
  • 29" role="presentation" style="box-sizing: border-box; user-select: initial !important; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">911911%
  • 19" role="presentation" style="box-sizing: border-box; user-select: initial !important; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">211211%

According to the passage given above the following information is obtained.

Stream

Students

Percentage

Science

-

-

Arts

1000

-

Agriculture

-

22.5%

Commerce

1200

15%

Total

-

100%

 

Let the total number of student in the college be x

∴ 15% of x = 1200

⇒ x = 8000

Total student in college is 8000

22.5% of total students are enrolled in the agriculture stream

∴ 22.5% of 8000 = 1800

There are 1800 students are enrolled in the agriculture stream

Let the percentage of arts students in the college is P

∴ P% of 8000 = 1000

⇒ P = 12.5%

Let the total number of student in the college is 100%

∴ Percentage of student in the science stream = 100% – (22.5% + 15% + 12.5%) = 50%

Total number of student in the science stream = 50% of 8000 = 4000

Now, we get the all the unknown values and formed the table

Stream

Students

Percentage

Science

4000

50%

Arts

1000

12.5%

Agriculture

1800

22.5%

Commerce

1200

15%

Total

8000

100%

 

We know that

Required percentage = (First quantity/Second Quantity) × 100

Number of student in science stream = 4000

Number of student in arts and commerce = 1000 + 1200 = 2200

∴ required percentage = ((4000 – 2200)/2200) × 100 = 81" role="presentation" style="box-sizing: border-box; user-select: initial !important; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">911911%

So, required percentage is 81" role="presentation" style="box-sizing: border-box; user-select: initial !important; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">911911%

Hence, option (1) is correct

6. Direction: Go through the passage given below and answer the question based on it.

There are four streams offered by a college viz. science, arts, agriculture, and commerce. 22.5% of total students are enrolled in the agriculture stream and there are 1000 students enrolled in the arts stream. The Commerce stream has 1200 students which are 15% of total students in the college.

Question:
Number of student in science stream is what percent of total student in college?
  • 25%
  • 50%
  • 60%
  • 30%
  • 35%

According to the passage given above the following information is obtained.

Stream

Students

Percentage

Science

-

-

Arts

1000

-

Agriculture

-

22.5%

Commerce

1200

15%

Total

-

100%

 

Let the total number of student in the college be x

∴ 15% of x = 1200

⇒ x = 8000

Total student in college is 8000

22.5% of total students are enrolled in the agriculture stream

∴ 22.5% of 8000 = 1800

There are 1800 students are enrolled in the agriculture stream

Let the percentage of arts students in the college is P

∴ P% of 8000 = 1000

⇒ P = 12.5%

Let the total number of student in the college is 100%

∴ Percentage of student in the science stream = 100% – (22.5% + 15% + 12.5%) = 50%

Total number of student in the science stream = 50% of 8000 = 4000

Now, we get the all the unknown values and formed the table

Stream

Students

Percentage

Science

4000

50%

Arts

1000

12.5%

Agriculture

1800

22.5%

Commerce

1200

15%

Total

8000

100%

 

Let the total number of student in the college is 100%

∴ Percentage of student in the science stream = 100% – (22.5% + 15% + 12.5%) = 50%

So, Number of student in science stream is 50% of total student in college.

Hence, option (2) is correct

7. Direction: Go through the passage given below and answer the question based on it.

There are four streams offered by a college viz. science, arts, agriculture, and commerce. 22.5% of total students are enrolled in the agriculture stream and there are 1000 students enrolled in the arts stream. The Commerce stream has 1200 students which are 15% of total students in the college.

Question:
The course fee of arts student is Rs. 4500 and commerce student is Rs. 5200. Find the difference in revenue received from both the courses?
  • Rs. 2460000
  • Rs. 4170000
  • Rs. 1740000
  • Rs. 3610000
  • Rs. 2100000

According to the passage given above the following information is obtained.

Stream

Students

Percentage

Science

-

-

Arts

1000

-

Agriculture

-

22.5%

Commerce

1200

15%

Total

-

100%

 

Let the total number of student in the college be x

∴ 15% of x = 1200

⇒ x = 8000

Total student in college is 8000

22.5% of total students are enrolled in the agriculture stream

∴ 22.5% of 8000 = 1800

There are 1800 students are enrolled in the agriculture stream

Let the percentage of arts students in the college is P

∴ P% of 8000 = 1000

⇒ P = 12.5%

Let the total number of student in the college is 100%

∴ Percentage of student in the science stream = 100% – (22.5% + 15% + 12.5%) = 50%

Total number of student in the science stream = 50% of 8000 = 4000

Now, we get the all the unknown values and formed the table

Stream

Students

Percentage

Science

4000

50%

Arts

1000

12.5%

Agriculture

1800

22.5%

Commerce

1200

15%

Total

8000

100%

 

Total student in arts = 1000

∴ Revenue received = 1000 × Rs. 4500 = Rs. 4500000

Total student in commerce = 1200

∴ Revenue received = 1200 × Rs. 5200 = Rs. 6240000

Required difference = Rs. 6240000 – Rs. 4500000 = Rs. 1740000

So, the required difference is Rs. 1740000

Hence, option (3) is correct

8. Directions: Read the following information carefully and answer the given questions:- 

There are two Indoor games such as Chess and Carrom played by some boys and girls. The total number of boys playing indoor games is 50 and the total number of girls playing indoor games is half the number of boys. At the event, 20% of the total boys and 40% of total girls have played in Chess. The remaining number of girls and boys played Carrom. One person can play only one game and everyone is playing.

Question:
Find the sum of number of boys who have played Carrom at the Event and number of girls who have played Chess at the Event.
  • 50
  • 30
  • 10
  • 15
  • 20
  Number of boys Number of girls
Chess 10 10
Carrom 40 15
Total 50 25

 

Number of boys who have played Carrom at the Event = 40

Number of girls who have played Chess at the Event = 10

∴  Required Sum = 40 + 10 = 50

9. Directions: Read the following information carefully and answer the given questions:- 

There are two Indoor games such as Chess and Carrom played by some boys and girls. The total number of boys playing indoor games is 50 and the total number of girls playing indoor games is half the number of boys. At the event, 20% of the total boys and 40% of total girls have played in Chess. The remaining number of girls and boys played Carrom. One person can play only one game and everyone is playing.

Question:
Find the ratio of boys and girls who have played Chess in the event.
  • 1 : 1
  • 1 : 2
  • 2 : 1
  • 8 : 3
  • 3 : 8

 

Number of boys

Number of girls

Chess

10

10

Carrom

40

15

Total

50

25

 

The number of boys playing Chess = 10

The number of girls playing Chess = 10

∴ Required ratio = 10 : 10 = 1 : 1

10. Directions: Read the following information carefully and answer the given questions:- 

There are two Indoor games such as Chess and Carrom played by some boys and girls. The total number of boys playing indoor games is 50 and the total number of girls playing indoor games is half the number of boys. At the event, 20% of the total boys and 40% of total girls have played in Chess. The remaining number of girls and boys played Carrom. One person can play only one game and everyone is playing.

Question:
Number of girls playing chess is what percent more/less than number of boys playing carrom.
  • 75%
  • 30%
  • 40%
  • 50%
  • 60%
  Number of boys
  Number of girls  
Chess 10 10
Carrom 40 15
Total 50 25


The number of girls playing chess = 10

The number of boys playing Carrom = 40

∴ required less percentage = (40 - 10)/40 × 100 = 30/40 × 100 = 75%

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