AAO ExamCT 13: Quant (DI  Caselet)
AAO ExamCT 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.
What percent male players playing cricket from the total number of male players?

37.35%

27.25%

40%

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

7 : 9

9 : 7

9 : 16

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

55

45

60

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.
What is the number of female players in football?

700

750

850

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.

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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="boxsizing: borderbox; userselect: initial !important; display: inline; fontstyle: normal; fontweight: normal; lineheight: normal; fontsize: 16px; textindent: 0px; textalign: left; texttransform: none; letterspacing: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: none; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">911$\frac{9}{11}$%
So, required percentage is 81" role="presentation" style="boxsizing: borderbox; userselect: initial !important; display: inline; fontstyle: normal; fontweight: normal; lineheight: normal; fontsize: 16px; textindent: 0px; textalign: left; texttransform: none; letterspacing: normal; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: none; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0">911$\frac{9}{11}$%
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.

25%

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.

Rs. 2460000

Rs. 4170000

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.

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.

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.

30%

40%

50%

60%
Number of boys 


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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