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 Page 1


IIFT 23rd Dec 2021 Slot 1
Quantitative Analysis
1. Rahul takes 4 days to finish one third of a job, Sohan takes 3 days to finish one sixth of thesame work and Ram takes 5 days to
finish half the job. All 3 of them together work for 3 days after whichRahul and Ram leave the job. How long will it take for
Sohan to complete the remaining work?
A    6 days
B    8.1 days
C    5.1 days
D    7 days
A n s w e r : C
Explanation:
From the above information, we can say that Rahul, Sohan and Ram take 12, 18 and 10 days respectively to complete the work alone.
LCM(12, 18, 10)= 180
Let the total work be 180 units
So Work done by Rahul in 1 day = 15 units
Work done by Sohan in 1 day = 10 units
Work done by Ram in 1 day = 18 units
Let the time taken by Sohan to complete the remaining work be x days.
Therefore, 180 = 3*(15+10+18) + 10x
or, 180 = 129 - 10x
or, x= 5.1 days
    
2. A shopkeeper marks up the price of the Toor dal by 20% and gives a discount of 10% to thecustomer. Besides, he also tricks
100 grams to his dealer and his customer respectively while buying orselling 1 kilogram of Toor dal. Find the profit percentage
of the shopkeeper.
A    22%
B    20%
C    32%
D    27%
A n s w e r : C
Explanation:
Let the cost of 1000gm of dal be rupees 1000
Now the shopkeeper is buying 1100 gm of dal for rupees 1000
While selling 900 gm of dal the shopkeeping is charging the price of 1000 gm
Therefore while selling 1100 gm of dal the shopkeeper will charge the price of (1000/900)*1100 gm = 11000/9 gm
He has marked up the price by 20% and then given a discount of 10%
So price charged by shopkeeper = (11000/9)*1.2*0.9 = 1320
  
.
Page 2


IIFT 23rd Dec 2021 Slot 1
Quantitative Analysis
1. Rahul takes 4 days to finish one third of a job, Sohan takes 3 days to finish one sixth of thesame work and Ram takes 5 days to
finish half the job. All 3 of them together work for 3 days after whichRahul and Ram leave the job. How long will it take for
Sohan to complete the remaining work?
A    6 days
B    8.1 days
C    5.1 days
D    7 days
A n s w e r : C
Explanation:
From the above information, we can say that Rahul, Sohan and Ram take 12, 18 and 10 days respectively to complete the work alone.
LCM(12, 18, 10)= 180
Let the total work be 180 units
So Work done by Rahul in 1 day = 15 units
Work done by Sohan in 1 day = 10 units
Work done by Ram in 1 day = 18 units
Let the time taken by Sohan to complete the remaining work be x days.
Therefore, 180 = 3*(15+10+18) + 10x
or, 180 = 129 - 10x
or, x= 5.1 days
    
2. A shopkeeper marks up the price of the Toor dal by 20% and gives a discount of 10% to thecustomer. Besides, he also tricks
100 grams to his dealer and his customer respectively while buying orselling 1 kilogram of Toor dal. Find the profit percentage
of the shopkeeper.
A    22%
B    20%
C    32%
D    27%
A n s w e r : C
Explanation:
Let the cost of 1000gm of dal be rupees 1000
Now the shopkeeper is buying 1100 gm of dal for rupees 1000
While selling 900 gm of dal the shopkeeping is charging the price of 1000 gm
Therefore while selling 1100 gm of dal the shopkeeper will charge the price of (1000/900)*1100 gm = 11000/9 gm
He has marked up the price by 20% and then given a discount of 10%
So price charged by shopkeeper = (11000/9)*1.2*0.9 = 1320
  
.
So the shopkeeper is spending rupees 1000 to buy the dal and is selling the same quantity of dal at rupees 1320. Therefore, profit
percentage is (320/1000)*100 = 32%
3. For maintaining social distancing due to covid situation, Rohan, Sohan and Rahul are sittingequidistantly, at a distance of 3
meter in a triangular formation. Priya came and sat in between Sohan andRahul such that distance between Priya and Sohan is
half the distance between Rahul and Priya. What willbe the distance between Priya and Rohan in meter?
A    
B    
C    
D    
A n s w e r : C
4. In a group of students, x number of students drink only Fruit Juice, 2x number of students drinkonly Coke.  students drink
both Fruit Juice and Coke and the students who drink neither Fruit Juice norCoke are . The number of students who drink
Coke may be
A    41 and 39
B    39 and 54
C    59 and 54
D    41 and 59
A n s w e r : D
Explanation:
No of persons who drink coke = 2x + 57/x
As the no. of persons who drink coke will be an integer so 57/x must be an integer so x can be 1, 3, 19 or 57.
No. of persons who drink neither fruit juice nor coke = 57/3x = 19/x this also should be an integer, so x= 1 or 19 only
When x=1, no. of persons who drink coke = 2+57 = 59
When x=19, no. of persons who drink coke = 38 + 3 = 41
    
5. Ishika speaks truth in 60% of cases and Mishika in 85% of cases. Ishika and Mishika agree in astatement. Find the probability
that the statement is true.
A    
B    
C    
D    
A n s w e r : D
Explanation:
For both Ishika and Mishika to agree on a statement either both have to speak the truth or both have to speak false.
Probability of both speaking truth = (60/100)*(85/100) = 204/400
5
6
7
8
x
57
3 x
57
57
49
100
51
100
57
57
51
  
.
Page 3


IIFT 23rd Dec 2021 Slot 1
Quantitative Analysis
1. Rahul takes 4 days to finish one third of a job, Sohan takes 3 days to finish one sixth of thesame work and Ram takes 5 days to
finish half the job. All 3 of them together work for 3 days after whichRahul and Ram leave the job. How long will it take for
Sohan to complete the remaining work?
A    6 days
B    8.1 days
C    5.1 days
D    7 days
A n s w e r : C
Explanation:
From the above information, we can say that Rahul, Sohan and Ram take 12, 18 and 10 days respectively to complete the work alone.
LCM(12, 18, 10)= 180
Let the total work be 180 units
So Work done by Rahul in 1 day = 15 units
Work done by Sohan in 1 day = 10 units
Work done by Ram in 1 day = 18 units
Let the time taken by Sohan to complete the remaining work be x days.
Therefore, 180 = 3*(15+10+18) + 10x
or, 180 = 129 - 10x
or, x= 5.1 days
    
2. A shopkeeper marks up the price of the Toor dal by 20% and gives a discount of 10% to thecustomer. Besides, he also tricks
100 grams to his dealer and his customer respectively while buying orselling 1 kilogram of Toor dal. Find the profit percentage
of the shopkeeper.
A    22%
B    20%
C    32%
D    27%
A n s w e r : C
Explanation:
Let the cost of 1000gm of dal be rupees 1000
Now the shopkeeper is buying 1100 gm of dal for rupees 1000
While selling 900 gm of dal the shopkeeping is charging the price of 1000 gm
Therefore while selling 1100 gm of dal the shopkeeper will charge the price of (1000/900)*1100 gm = 11000/9 gm
He has marked up the price by 20% and then given a discount of 10%
So price charged by shopkeeper = (11000/9)*1.2*0.9 = 1320
  
.
So the shopkeeper is spending rupees 1000 to buy the dal and is selling the same quantity of dal at rupees 1320. Therefore, profit
percentage is (320/1000)*100 = 32%
3. For maintaining social distancing due to covid situation, Rohan, Sohan and Rahul are sittingequidistantly, at a distance of 3
meter in a triangular formation. Priya came and sat in between Sohan andRahul such that distance between Priya and Sohan is
half the distance between Rahul and Priya. What willbe the distance between Priya and Rohan in meter?
A    
B    
C    
D    
A n s w e r : C
4. In a group of students, x number of students drink only Fruit Juice, 2x number of students drinkonly Coke.  students drink
both Fruit Juice and Coke and the students who drink neither Fruit Juice norCoke are . The number of students who drink
Coke may be
A    41 and 39
B    39 and 54
C    59 and 54
D    41 and 59
A n s w e r : D
Explanation:
No of persons who drink coke = 2x + 57/x
As the no. of persons who drink coke will be an integer so 57/x must be an integer so x can be 1, 3, 19 or 57.
No. of persons who drink neither fruit juice nor coke = 57/3x = 19/x this also should be an integer, so x= 1 or 19 only
When x=1, no. of persons who drink coke = 2+57 = 59
When x=19, no. of persons who drink coke = 38 + 3 = 41
    
5. Ishika speaks truth in 60% of cases and Mishika in 85% of cases. Ishika and Mishika agree in astatement. Find the probability
that the statement is true.
A    
B    
C    
D    
A n s w e r : D
Explanation:
For both Ishika and Mishika to agree on a statement either both have to speak the truth or both have to speak false.
Probability of both speaking truth = (60/100)*(85/100) = 204/400
5
6
7
8
x
57
3 x
57
57
49
100
51
100
57
57
51
  
.
Probability of both speaking false = (40/100)*(15/100) = 24/400
The probability that the statement is true when Ishika and Mishika both agree on a statement = (204/400)/{(204/400)+(24/400)} =
204/228 = 51/57
6. The last two digits of the expression 
A    61
B    71
C    81
D    91
A n s w e r : C
Explanation:
From the 5th term onwards the last two of all the terms will 00.
The last two digits of 24 to the power of an even number will be 76 always.
So, last two digits of the above expression will be the last two digits of 
=1+8+139968+304= 140281
So last two digits is 81
7. Two towers 10 meters apart, are 4 m and 6 m high respectively. What will be the height of pointof intersection of lines joining
the top of each tower to the bottom of opposite tower?
A    2.2 meters
B    1.5 meters
C    5.5 meters
D    2.4 meters
A n s w e r : D
Explanation:
Let AB and CD be the towers of length 4m and 6m respectively. 
Let the length of BF be x therefore, the length of FC will be 10-x.
Triangle BEF is similar to triangle BDC
So, 
or, 
Therefore, 
Similarly, triangle EFC is similar to triangle ABC
1(1!) +
1!
2(2!) +
2!
3(3!) +
3!
.... + 121(121!)
121!
1 + 2 2 + ( )
2
3 6 + ( )
6
4 76 ( )
= D C
E F
= B C
B F
B D
B E
= 6
E F
= 10
x
B D
B E
E F = 5
3 x
E F C F E C
  
.
Page 4


IIFT 23rd Dec 2021 Slot 1
Quantitative Analysis
1. Rahul takes 4 days to finish one third of a job, Sohan takes 3 days to finish one sixth of thesame work and Ram takes 5 days to
finish half the job. All 3 of them together work for 3 days after whichRahul and Ram leave the job. How long will it take for
Sohan to complete the remaining work?
A    6 days
B    8.1 days
C    5.1 days
D    7 days
A n s w e r : C
Explanation:
From the above information, we can say that Rahul, Sohan and Ram take 12, 18 and 10 days respectively to complete the work alone.
LCM(12, 18, 10)= 180
Let the total work be 180 units
So Work done by Rahul in 1 day = 15 units
Work done by Sohan in 1 day = 10 units
Work done by Ram in 1 day = 18 units
Let the time taken by Sohan to complete the remaining work be x days.
Therefore, 180 = 3*(15+10+18) + 10x
or, 180 = 129 - 10x
or, x= 5.1 days
    
2. A shopkeeper marks up the price of the Toor dal by 20% and gives a discount of 10% to thecustomer. Besides, he also tricks
100 grams to his dealer and his customer respectively while buying orselling 1 kilogram of Toor dal. Find the profit percentage
of the shopkeeper.
A    22%
B    20%
C    32%
D    27%
A n s w e r : C
Explanation:
Let the cost of 1000gm of dal be rupees 1000
Now the shopkeeper is buying 1100 gm of dal for rupees 1000
While selling 900 gm of dal the shopkeeping is charging the price of 1000 gm
Therefore while selling 1100 gm of dal the shopkeeper will charge the price of (1000/900)*1100 gm = 11000/9 gm
He has marked up the price by 20% and then given a discount of 10%
So price charged by shopkeeper = (11000/9)*1.2*0.9 = 1320
  
.
So the shopkeeper is spending rupees 1000 to buy the dal and is selling the same quantity of dal at rupees 1320. Therefore, profit
percentage is (320/1000)*100 = 32%
3. For maintaining social distancing due to covid situation, Rohan, Sohan and Rahul are sittingequidistantly, at a distance of 3
meter in a triangular formation. Priya came and sat in between Sohan andRahul such that distance between Priya and Sohan is
half the distance between Rahul and Priya. What willbe the distance between Priya and Rohan in meter?
A    
B    
C    
D    
A n s w e r : C
4. In a group of students, x number of students drink only Fruit Juice, 2x number of students drinkonly Coke.  students drink
both Fruit Juice and Coke and the students who drink neither Fruit Juice norCoke are . The number of students who drink
Coke may be
A    41 and 39
B    39 and 54
C    59 and 54
D    41 and 59
A n s w e r : D
Explanation:
No of persons who drink coke = 2x + 57/x
As the no. of persons who drink coke will be an integer so 57/x must be an integer so x can be 1, 3, 19 or 57.
No. of persons who drink neither fruit juice nor coke = 57/3x = 19/x this also should be an integer, so x= 1 or 19 only
When x=1, no. of persons who drink coke = 2+57 = 59
When x=19, no. of persons who drink coke = 38 + 3 = 41
    
5. Ishika speaks truth in 60% of cases and Mishika in 85% of cases. Ishika and Mishika agree in astatement. Find the probability
that the statement is true.
A    
B    
C    
D    
A n s w e r : D
Explanation:
For both Ishika and Mishika to agree on a statement either both have to speak the truth or both have to speak false.
Probability of both speaking truth = (60/100)*(85/100) = 204/400
5
6
7
8
x
57
3 x
57
57
49
100
51
100
57
57
51
  
.
Probability of both speaking false = (40/100)*(15/100) = 24/400
The probability that the statement is true when Ishika and Mishika both agree on a statement = (204/400)/{(204/400)+(24/400)} =
204/228 = 51/57
6. The last two digits of the expression 
A    61
B    71
C    81
D    91
A n s w e r : C
Explanation:
From the 5th term onwards the last two of all the terms will 00.
The last two digits of 24 to the power of an even number will be 76 always.
So, last two digits of the above expression will be the last two digits of 
=1+8+139968+304= 140281
So last two digits is 81
7. Two towers 10 meters apart, are 4 m and 6 m high respectively. What will be the height of pointof intersection of lines joining
the top of each tower to the bottom of opposite tower?
A    2.2 meters
B    1.5 meters
C    5.5 meters
D    2.4 meters
A n s w e r : D
Explanation:
Let AB and CD be the towers of length 4m and 6m respectively. 
Let the length of BF be x therefore, the length of FC will be 10-x.
Triangle BEF is similar to triangle BDC
So, 
or, 
Therefore, 
Similarly, triangle EFC is similar to triangle ABC
1(1!) +
1!
2(2!) +
2!
3(3!) +
3!
.... + 121(121!)
121!
1 + 2 2 + ( )
2
3 6 + ( )
6
4 76 ( )
= D C
E F
= B C
B F
B D
B E
= 6
E F
= 10
x
B D
B E
E F = 5
3 x
E F C F E C
  
.
So, 
or, 
or, 
Therefore, 
or, 
EF= 
   
8. , where y = f(x). Find the ratio of x to f(y).
A    
B    
C    1 : 2
D    1 : 1
A n s w e r : D
Explanation:
or, 
or, 
Therefore x:f(y) = 1:1
9. During a marriage ceremony in Panipat, two shots from the air rifle are fired from the sameplace at an interval of 10 minutes 42
seconds. A man sitting in the train which is approaching the placewhere the ceremony is being held, hears the second sound
after 10 minutes of hearing the first one.Assuming speed of sound to be 330 m/s, what could be the speed of the train?
A    20.1 m/s
B    12.4 m/s
C    23.1 m/s
D    30.1 m/s
A n s w e r : C
Explanation:
Distance travelled by the train till the man hears the two shots = m
This distance was travelled by train in 10 minutes or 600 seconds
Speed of train = 13860/600 = 23.1 m/s
10. If area of the adjacent faces of a cuboid is given as p, q and r respectively and the volume isgiven as 'V' then the square of the
volume will be
A    
= A B
E F
= B C
C F
A C
E C
= 4
E F
= 10
10- x
A C
E C
E F = 5
2 10- x ( )
= 5
2 10- x ( )
5
3 x
x = 4
= 5
3 x
2.4 m
f( x) = 2 x-2
2 x+2
:
x
y
x :
3
y
3
f y = ( ) f f x ( ( ))
f y = ( ) f ( 2 x-2
2 x+2
)
f y = ( )
2 -2 ( 2 x-2
2 x+2
)
2 +2 ( 2 x-2
2 x+2
)
f y = ( ) = 8
8 x
x
42 × 330 = 13860
p q r
q r
  
.
Page 5


IIFT 23rd Dec 2021 Slot 1
Quantitative Analysis
1. Rahul takes 4 days to finish one third of a job, Sohan takes 3 days to finish one sixth of thesame work and Ram takes 5 days to
finish half the job. All 3 of them together work for 3 days after whichRahul and Ram leave the job. How long will it take for
Sohan to complete the remaining work?
A    6 days
B    8.1 days
C    5.1 days
D    7 days
A n s w e r : C
Explanation:
From the above information, we can say that Rahul, Sohan and Ram take 12, 18 and 10 days respectively to complete the work alone.
LCM(12, 18, 10)= 180
Let the total work be 180 units
So Work done by Rahul in 1 day = 15 units
Work done by Sohan in 1 day = 10 units
Work done by Ram in 1 day = 18 units
Let the time taken by Sohan to complete the remaining work be x days.
Therefore, 180 = 3*(15+10+18) + 10x
or, 180 = 129 - 10x
or, x= 5.1 days
    
2. A shopkeeper marks up the price of the Toor dal by 20% and gives a discount of 10% to thecustomer. Besides, he also tricks
100 grams to his dealer and his customer respectively while buying orselling 1 kilogram of Toor dal. Find the profit percentage
of the shopkeeper.
A    22%
B    20%
C    32%
D    27%
A n s w e r : C
Explanation:
Let the cost of 1000gm of dal be rupees 1000
Now the shopkeeper is buying 1100 gm of dal for rupees 1000
While selling 900 gm of dal the shopkeeping is charging the price of 1000 gm
Therefore while selling 1100 gm of dal the shopkeeper will charge the price of (1000/900)*1100 gm = 11000/9 gm
He has marked up the price by 20% and then given a discount of 10%
So price charged by shopkeeper = (11000/9)*1.2*0.9 = 1320
  
.
So the shopkeeper is spending rupees 1000 to buy the dal and is selling the same quantity of dal at rupees 1320. Therefore, profit
percentage is (320/1000)*100 = 32%
3. For maintaining social distancing due to covid situation, Rohan, Sohan and Rahul are sittingequidistantly, at a distance of 3
meter in a triangular formation. Priya came and sat in between Sohan andRahul such that distance between Priya and Sohan is
half the distance between Rahul and Priya. What willbe the distance between Priya and Rohan in meter?
A    
B    
C    
D    
A n s w e r : C
4. In a group of students, x number of students drink only Fruit Juice, 2x number of students drinkonly Coke.  students drink
both Fruit Juice and Coke and the students who drink neither Fruit Juice norCoke are . The number of students who drink
Coke may be
A    41 and 39
B    39 and 54
C    59 and 54
D    41 and 59
A n s w e r : D
Explanation:
No of persons who drink coke = 2x + 57/x
As the no. of persons who drink coke will be an integer so 57/x must be an integer so x can be 1, 3, 19 or 57.
No. of persons who drink neither fruit juice nor coke = 57/3x = 19/x this also should be an integer, so x= 1 or 19 only
When x=1, no. of persons who drink coke = 2+57 = 59
When x=19, no. of persons who drink coke = 38 + 3 = 41
    
5. Ishika speaks truth in 60% of cases and Mishika in 85% of cases. Ishika and Mishika agree in astatement. Find the probability
that the statement is true.
A    
B    
C    
D    
A n s w e r : D
Explanation:
For both Ishika and Mishika to agree on a statement either both have to speak the truth or both have to speak false.
Probability of both speaking truth = (60/100)*(85/100) = 204/400
5
6
7
8
x
57
3 x
57
57
49
100
51
100
57
57
51
  
.
Probability of both speaking false = (40/100)*(15/100) = 24/400
The probability that the statement is true when Ishika and Mishika both agree on a statement = (204/400)/{(204/400)+(24/400)} =
204/228 = 51/57
6. The last two digits of the expression 
A    61
B    71
C    81
D    91
A n s w e r : C
Explanation:
From the 5th term onwards the last two of all the terms will 00.
The last two digits of 24 to the power of an even number will be 76 always.
So, last two digits of the above expression will be the last two digits of 
=1+8+139968+304= 140281
So last two digits is 81
7. Two towers 10 meters apart, are 4 m and 6 m high respectively. What will be the height of pointof intersection of lines joining
the top of each tower to the bottom of opposite tower?
A    2.2 meters
B    1.5 meters
C    5.5 meters
D    2.4 meters
A n s w e r : D
Explanation:
Let AB and CD be the towers of length 4m and 6m respectively. 
Let the length of BF be x therefore, the length of FC will be 10-x.
Triangle BEF is similar to triangle BDC
So, 
or, 
Therefore, 
Similarly, triangle EFC is similar to triangle ABC
1(1!) +
1!
2(2!) +
2!
3(3!) +
3!
.... + 121(121!)
121!
1 + 2 2 + ( )
2
3 6 + ( )
6
4 76 ( )
= D C
E F
= B C
B F
B D
B E
= 6
E F
= 10
x
B D
B E
E F = 5
3 x
E F C F E C
  
.
So, 
or, 
or, 
Therefore, 
or, 
EF= 
   
8. , where y = f(x). Find the ratio of x to f(y).
A    
B    
C    1 : 2
D    1 : 1
A n s w e r : D
Explanation:
or, 
or, 
Therefore x:f(y) = 1:1
9. During a marriage ceremony in Panipat, two shots from the air rifle are fired from the sameplace at an interval of 10 minutes 42
seconds. A man sitting in the train which is approaching the placewhere the ceremony is being held, hears the second sound
after 10 minutes of hearing the first one.Assuming speed of sound to be 330 m/s, what could be the speed of the train?
A    20.1 m/s
B    12.4 m/s
C    23.1 m/s
D    30.1 m/s
A n s w e r : C
Explanation:
Distance travelled by the train till the man hears the two shots = m
This distance was travelled by train in 10 minutes or 600 seconds
Speed of train = 13860/600 = 23.1 m/s
10. If area of the adjacent faces of a cuboid is given as p, q and r respectively and the volume isgiven as 'V' then the square of the
volume will be
A    
= A B
E F
= B C
C F
A C
E C
= 4
E F
= 10
10- x
A C
E C
E F = 5
2 10- x ( )
= 5
2 10- x ( )
5
3 x
x = 4
= 5
3 x
2.4 m
f( x) = 2 x-2
2 x+2
:
x
y
x :
3
y
3
f y = ( ) f f x ( ( ))
f y = ( ) f ( 2 x-2
2 x+2
)
f y = ( )
2 -2 ( 2 x-2
2 x+2
)
2 +2 ( 2 x-2
2 x+2
)
f y = ( ) = 8
8 x
x
42 × 330 = 13860
p q r
q r
  
.
B    
C    
D    
A n s w e r : A
Explanation:
Let the length, breadth and height of the cubhoid be l, b and h respectively.
Therefore of adjacent faces will be lb, bh and hl.
If lb= p, then bh= q and hl=r.
Volume (V) = lbh
or, 
      
11. If a principal P amounts to A in two years when compounded half yearly with r% interest. The same principal P amounts to A in
two years when compounded annually with R% interest, then which of the following relationship is true?
A    
B    
C    
D    
A n s w e r : C
Explanation:
Since in first case we are compounding half-yearly and in second case we are compounding yearly and the amount received and the
principal invested in both the cases is same so interest rate in the first case is lower than the interest rate in the second case.
12. In the galaxy “Andromeda”, a planet named “Exo” has a city called “Azith”. The city has analphabet system that consists of 48
letters and an octo-decimal number system (base -18). Theregistration number on the number plate of a vehicle in the city has
two parts. The first part is the alphabetpart that consists of three letters and the second part is the number part that consists of
3 digits. The cityadministration issues all kinds of registration numbers with following restrictions:
a. The letters in the alphabet part are in ascending order and all letters must be distinct.
b. In the number part, the first digit is three more than the third digit.
Find the number of possible registration numbers available in the Azith city.
A    3353270
B    2557830
C    5339840
D    4669920
A n s w e r : D
Explanation:
There are 48 alphabets out of which we need 3
So, no. of ways of selecting 3 alphabets from 48 alphabets is 
Since we need to arrange these alphabets in ascending order so there is only one possible way for every three alphabets.
p
2
q r
r
2
( p q)
2
( p q r)
2
V =
2
l b h ( )
2
V =
2
p q r
r > R
r = R
r < R
r = R
C
48
3
  
.
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