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Logical Reasoning · Data Arrangements and Blood Relations

Data Arrangements - Formulas, Key Points and formulas

Explanation

🔵
 DATA ARRANGEMENTS\text{ DATA ARRANGEMENTS}
🟢 1. BASIC DATA ARRANGEMENT Data arrangement questions require arranging given information according to specific conditions.
Data Arrangement=Organizing given information according to the conditions \text{Data Arrangement} = \text{Organizing given information according to the conditions}
The information may involve:
Persons, Objects, Places, Numbers, Days, Ranks or Positions \text{Persons, Objects, Places, Numbers, Days, Ranks or Positions}
🟡 KEY POINT
Read all the conditions carefully before starting the arrangement. \text{Read all the conditions carefully before starting the arrangement.}
🟢 2. LINEAR ARRANGEMENT In a linear arrangement, people or objects are arranged in a straight line. For example:
ABCDE A\quad B\quad C\quad D\quad E
If AA is to the left of BB:
AB A\quad B
If AA is immediately to the right of BB:
BA B\quad A
🟡 KEY POINT
Left and right depend on the direction specified in the question. \text{Left and right depend on the direction specified in the question.}
🟢 3. POSITION IN A LINE If a person is at position PP from the left in a row of NN persons, the position from the right is:
Position from Right=N−P+1 \text{Position from Right} = N-P+1
Similarly:
Position from Left=N−P+1 \text{Position from Left} = N-P+1
if the position from the right is known. 🟡 KEY POINT
Position from opposite side=Total Persons−Known Position+1 \text{Position from opposite side} = \text{Total Persons}-\text{Known Position}+1
🟢 4. NUMBER OF PERSONS BETWEEN TWO POSITIONS If two persons occupy positions P1P_1 and P2P_2:
Persons Between=∣P1−P2∣−1 \text{Persons Between} = |P_1-P_2|-1
For example, if two persons are at positions 4 and 9:
∣9−4∣−1 |9-4|-1
=5−1 =5-1
=4 =4
🟡 KEY POINT
Always subtract 1 when finding the number of persons between two positions. \text{Always subtract 1 when finding the number of persons between two positions.}
🟢 5. IMMEDIATE LEFT AND RIGHT If AA is immediately left of BB:
AB A\quad B
If AA is immediately right of BB:
BA B\quad A
The word "immediately" means there is no person or object between them. 🟡 KEY POINT
Immediate left/right means adjacent positions. \text{Immediate left/right means adjacent positions.}
🟢 6. SECOND TO THE LEFT OR RIGHT If AA is second to the left of BB, exactly one position lies between them.
AXB A\quad X\quad B
If AA is second to the right of BB:
BXA B\quad X\quad A
🟡 KEY POINT
Second position means one person or object lies between them. \text{Second position means one person or object lies between them.}
🟢 7. THIRD POSITION If AA is third to the left of BB:
AXXB A\quad X\quad X\quad B
There are two positions between them. Therefore:
Persons Between=3−1 \text{Persons Between}=3-1
=2 =2
🟢 8. ORDER AND RANKING Ranking questions involve the position of a person or object according to a particular order. If a person ranks PP from the top in a group of NN persons:
Rank from Bottom=N−P+1 \text{Rank from Bottom} = N-P+1
If a person ranks PP from the bottom:
Rank from Top=N−P+1 \text{Rank from Top} = N-P+1
🟡 KEY POINT
Opposite Rank=Total Number−Known Rank+1 \text{Opposite Rank} = \text{Total Number}-\text{Known Rank}+1
🟢 9. TOTAL NUMBER FROM TWO RANKS If a person's rank from the top is PP and from the bottom is QQ:
Total Persons=P+Q−1 \text{Total Persons} = P+Q-1
The subtraction of 1 is necessary because the same person is counted in both ranks. 🟡 KEY POINT
Total=Top Rank+Bottom Rank−1 \text{Total}= \text{Top Rank}+\text{Bottom Rank}-1
🟢 10. CIRCULAR ARRANGEMENT In a circular arrangement, people or objects are arranged around a circle. For example:
ABCD A\quad B\quad C\quad D
may be arranged around a circle. In circular arrangements, relative positions are more important than absolute positions. 🟡 KEY POINT
There is no fixed leftmost or rightmost position in a circle. \text{There is no fixed leftmost or rightmost position in a circle.}
🟢 11. CLOCKWISE AND ANTICLOCKWISE Clockwise means moving in the same direction as the hands of a clock.
Clockwise=Direction of clock hands \text{Clockwise} = \text{Direction of clock hands}
Anticlockwise means moving in the opposite direction.
Anticlockwise=Opposite direction to clock hands \text{Anticlockwise} = \text{Opposite direction to clock hands}
🟡 KEY POINT
Always identify the facing direction before deciding left and right. \text{Always identify the facing direction before deciding left and right.}
🟢 12. FACING THE CENTRE When people face the centre of a circle:
Left and Right are determined from the person’s own perspective. \text{Left and Right are determined from the person's own perspective.}
For a person facing the centre:
Left side=Clockwise direction \text{Left side} = \text{Clockwise direction}
Right side=Anticlockwise direction \text{Right side} = \text{Anticlockwise direction}
🟡 KEY POINT
For people facing the centre, left is clockwise and right is anticlockwise. \text{For people facing the centre, left is clockwise and right is anticlockwise.}
🟢 13. FACING OUTSIDE When people face away from the centre:
Left side=Anticlockwise direction \text{Left side} = \text{Anticlockwise direction}
Right side=Clockwise direction \text{Right side} = \text{Clockwise direction}
🟡 KEY POINT
For people facing outside, left and right are reversed. \text{For people facing outside, left and right are reversed.}
🟢 14. FIXED POSITION A condition may directly specify a person's position. For example:
A is at the extreme left. A\text{ is at the extreme left.}
Then:
A____ A\quad \_\quad \_\quad \_\quad \_
If BB is at the extreme right:
A___B A\quad \_\quad \_\quad \_\quad B
🟡 KEY POINT
Place fixed positions first. \text{Place fixed positions first.}
🟢 15. BETWEEN TWO PERSONS If AA is between BB and CC:
BAC B\quad A\quad C
or:
CAB C\quad A\quad B
The exact order depends on additional conditions. 🟡 KEY POINT
"Between" does not always mean immediately between. \text{"Between"}\text{ does not always mean immediately between.}
🟢 16. ADJACENT POSITIONS Two people are adjacent when they occupy consecutive positions.
AB A\quad B
There is no person between them. Therefore:
Number of Persons Between=0 \text{Number of Persons Between}=0
🟢 17. NOT ADJACENT If two persons are not adjacent:
AXB A\quad X\quad B
At least one person or object must be between them.
Persons Between≥1 \text{Persons Between}\geq1
🟢 18. ORDERING BY AGE, HEIGHT OR WEIGHT Data arrangement can involve ordering people according to measurable characteristics. For increasing order:
A<B<C<D A<B<C<D
For decreasing order:
D>C>B>A D>C>B>A
🟡 KEY POINT
Convert every comparison into a clear order before solving. \text{Convert every comparison into a clear order before solving.}
🟢 19. COMPARISON STATEMENTS If AA is taller than BB:
A>B A>B
If CC is shorter than AA:
C<A C<A
Therefore:
A>C A>C
If:
A>B>C A>B>C
then:
A>B A>B
B>C B>C
and:
A>C A>C
🟢 20. CONDITIONAL ARRANGEMENT Some questions contain conditions such as:
A sits to the left of B. A\text{ sits to the left of }B.
C sits immediately right of D. C\text{ sits immediately right of }D.
E is not at an extreme position. E\text{ is not at an extreme position.}
All conditions must be satisfied simultaneously. 🟡 KEY POINT
Do not solve each condition separately without checking the complete arrangement. \text{Do not solve each condition separately without checking the complete arrangement.}
🟢 21. GROUPING ARRANGEMENT Some questions require placing people or objects into groups. For example:
Group 1: A,B,C \text{Group 1}:\ A,B,C
Group 2: D,E,F \text{Group 2}:\ D,E,F
If AA and BB must be together:
(A,B) (A,B)
can be treated as one unit during the initial arrangement. 🟡 KEY POINT
Combine items that must stay together into a block. \text{Combine items that must stay together into a block.}
🟢 22. DAYS AND SCHEDULE ARRANGEMENT Data arrangement may involve assigning activities to different days. For example:
Monday→A \text{Monday}\rightarrow A
Tuesday→B \text{Tuesday}\rightarrow B
Wednesday→C \text{Wednesday}\rightarrow C
Conditions may specify before, after, immediately before or immediately after. 🟡 KEY POINT
Before and after conditions should be converted into positional relationships. \text{Before and after conditions should be converted into positional relationships.}
🟢 23. BEFORE AND AFTER If AA occurs before BB:
A<B A<B
If CC occurs after BB:
B<C B<C
Therefore:
A<B<C A<B<C
🟡 KEY POINT
Before/after relationships help create an order chain. \text{Before/after relationships help create an order chain.}
🟢 24. IMMEDIATELY BEFORE AND AFTER If AA occurs immediately before BB:
AB A\quad B
If CC occurs immediately after DD:
DC D\quad C
🟡 KEY POINT
"Immediately before/after" means consecutive positions. \text{"Immediately before/after"}\text{ means consecutive positions.}
🟢 25. EXTREME POSITIONS In a row, the extreme positions are:
First Position and Last Position \text{First Position and Last Position}
For NN positions:
First Position=1 \text{First Position}=1
Last Position=N \text{Last Position}=N
🟡 KEY POINT
Check extreme positions before filling middle positions. \text{Check extreme positions before filling middle positions.}
🟢 26. MIDDLE POSITION If there are NN positions and NN is odd, the middle position is:
Middle Position=N+12 \text{Middle Position} = \frac{N+1}{2}
For example, for 9 positions:
9+12=5 \frac{9+1}{2}=5
Therefore:
Middle Position=5 \text{Middle Position}=5
🟢 27. TWO MIDDLE POSITIONS If the number of positions is even, there are two middle positions. For NN positions:
Middle Positions=N2andN2+1 \text{Middle Positions} = \frac{N}{2} \quad\text{and}\quad \frac{N}{2}+1
For 10 positions:
102=5 \frac{10}{2}=5
and:
5+1=6 5+1=6
Therefore:
Middle Positions=5 and 6 \text{Middle Positions}=5\text{ and }6
🟢 28. POSITION FROM BOTH ENDS If there are NN people and a person is at position PP from the left:
Position from Right=N−P+1 \text{Position from Right} = N-P+1
If the position from the right is QQ:
Position from Left=N−Q+1 \text{Position from Left} = N-Q+1
🟢 29. NUMBER OF PEOPLE BETWEEN TWO PEOPLE If two people are at positions PP and QQ:
Number Between=∣P−Q∣−1 \text{Number Between} = |P-Q|-1
If they are at positions 3 and 8:
∣8−3∣−1 |8-3|-1
=4 =4
Therefore:
Number Between=4 \text{Number Between}=4
🟢 30. BEST METHOD TO SOLVE DATA ARRANGEMENT First identify the type of arrangement.
Linear \text{Linear}
Circular \text{Circular}
Ranking \text{Ranking}
Grouping \text{Grouping}
Scheduling \text{Scheduling}
Then:
Step 1: Identify fixed information \text{Step 1: Identify fixed information}
Step 2: Place definite positions \text{Step 2: Place definite positions}
Step 3: Create blocks for linked information \text{Step 3: Create blocks for linked information}
Step 4: Apply remaining conditions \text{Step 4: Apply remaining conditions}
Step 5: Check every condition \text{Step 5: Check every condition}
Step 6: Answer the question \text{Step 6: Answer the question}
🟡 IMPORTANT KEY POINTS
Read every condition carefully. \text{Read every condition carefully.}
Place fixed positions first. \text{Place fixed positions first.}
Use blocks for people who must be together. \text{Use blocks for people who must be together.}
Use position numbers to avoid confusion. \text{Use position numbers to avoid confusion.}
For opposite rank, use N−P+1. \text{For opposite rank, use }N-P+1.
For people between two positions, use ∣P−Q∣−1. \text{For people between two positions, use }|P-Q|-1.
For circular arrangements, identify the facing direction first. \text{For circular arrangements, identify the facing direction first.}
For centre-facing people, left is clockwise and right is anticlockwise. \text{For centre-facing people, left is clockwise and right is anticlockwise.}
For outside-facing people, left is anticlockwise and right is clockwise. \text{For outside-facing people, left is anticlockwise and right is clockwise.}
Always verify the complete arrangement before selecting the answer. \text{Always verify the complete arrangement before selecting the answer.}

Example

🔵
DATA ARRANGEMENTS — SOLVED EXAMPLES\text{DATA ARRANGEMENTS — SOLVED EXAMPLES}
🟢 EXAMPLE 1: POSITION FROM THE RIGHT QUESTION: There are 25 students in a row. Ravi is 8th from the left. Find his position from the right. SOLUTION:
Position from Right=Total Students−Position from Left+1 \text{Position from Right} = \text{Total Students}-\text{Position from Left}+1
=25−8+1 = 25-8+1
=18 =18
🔵 ANSWER:
18th from the right 18\text{th from the right}
🟢 EXAMPLE 2: TOTAL NUMBER FROM TWO RANKS QUESTION: A student ranks 12th from the top and 19th from the bottom. Find the total number of students. SOLUTION:
Total Students=Top Rank+Bottom Rank−1 \text{Total Students} = \text{Top Rank}+\text{Bottom Rank}-1
=12+19−1 = 12+19-1
=30 =30
🔵 ANSWER:
30 students 30\text{ students}
🟢 EXAMPLE 3: PERSONS BETWEEN TWO POSITIONS QUESTION: In a row of students, Arun is 6th from the left and Kumar is 14th from the left. How many students are between them? SOLUTION:
Students Between=∣P1−P2∣−1 \text{Students Between} = |P_1-P_2|-1
=∣14−6∣−1 = |14-6|-1
=8−1 =8-1
=7 =7
🔵 ANSWER:
7 students 7\text{ students}
🟢 EXAMPLE 4: IMMEDIATE LEFT QUESTION: Five people A, B, C, D and E are standing in a row. B is immediately to the right of A. If A is at the extreme left, find the possible arrangement. SOLUTION: Since A is at the extreme left:
A____ A\quad\_\quad\_\quad\_\quad\_
B is immediately to the right of A:
AB___ A\quad B\quad\_\quad\_\quad\_
The remaining people are C, D and E. One possible arrangement is:
ABCDE A\quad B\quad C\quad D\quad E
🔵 ANSWER:
ABCDE A\quad B\quad C\quad D\quad E
🟢 EXAMPLE 5: SECOND TO THE LEFT QUESTION: A is second to the left of B. If B is in position 6, find the position of A. SOLUTION: Second to the left means two positions away.
Position of A=6−2 \text{Position of A} = 6-2
=4 =4
The arrangement is:
AXB A\quad X\quad B
🔵 ANSWER:
A is in position 4 \text{A is in position }4
🟢 EXAMPLE 6: THIRD TO THE RIGHT QUESTION: P is third to the right of Q. If Q is in position 4, find the position of P. SOLUTION:
Position of P=4+3 \text{Position of P} = 4+3
=7 =7
🔵 ANSWER:
P is in position 7 \text{P is in position }7
🟢 EXAMPLE 7: NUMBER OF PEOPLE BETWEEN TWO PEOPLE QUESTION: In a row of 20 people, A is 5th from the left and B is 17th from the left. How many people are between A and B? SOLUTION:
People Between=∣17−5∣−1 \text{People Between} = |17-5|-1
=12−1 =12-1
=11 =11
🔵 ANSWER:
11 people 11\text{ people}
🟢 EXAMPLE 8: RANK FROM THE BOTTOM QUESTION: Priya ranks 9th from the top in a class of 35 students. Find her rank from the bottom. SOLUTION:
Rank from Bottom=35−9+1 \text{Rank from Bottom} = 35-9+1
=27 =27
🔵 ANSWER:
27th from the bottom 27\text{th from the bottom}
🟢 EXAMPLE 9: RANK FROM THE TOP QUESTION: A student ranks 15th from the bottom in a class of 40 students. Find the rank from the top. SOLUTION:
Rank from Top=40−15+1 \text{Rank from Top} = 40-15+1
=26 =26
🔵 ANSWER:
26th from the top 26\text{th from the top}
🟢 EXAMPLE 10: MIDDLE POSITION QUESTION: Seven people are standing in a row. Which position is the middle position? SOLUTION:
Middle Position=N+12 \text{Middle Position} = \frac{N+1}{2}
=7+12 = \frac{7+1}{2}
=4 =4
🔵 ANSWER:
4th position 4\text{th position}
🟢 EXAMPLE 11: TWO MIDDLE POSITIONS QUESTION: Ten people are standing in a row. Find the two middle positions. SOLUTION:
First Middle Position=102 \text{First Middle Position} = \frac{10}{2}
=5 =5
Second middle position:
=5+1 =5+1
=6 =6
🔵 ANSWER:
5th and 6th positions 5\text{th and }6\text{th positions}
🟢 EXAMPLE 12: ORDER BY HEIGHT QUESTION: A is taller than B. C is taller than A. D is shorter than B. Arrange them from tallest to shortest. SOLUTION: Given:
C>A C>A
and:
A>B A>B
and:
B>D B>D
Therefore:
C>A>B>D C>A>B>D
🔵 ANSWER:
C>A>B>D C>A>B>D
🟢 EXAMPLE 13: ORDER BY AGE QUESTION: P is older than Q. R is younger than Q. S is older than P. Arrange them from oldest to youngest. SOLUTION: Given:
S>P S>P
P>Q P>Q
Q>R Q>R
Therefore:
S>P>Q>R S>P>Q>R
🔵 ANSWER:
S>P>Q>R S>P>Q>R
🟢 EXAMPLE 14: BEFORE AND AFTER QUESTION: Five subjects are scheduled from Monday to Friday. Mathematics is before English. Science is after English. If Mathematics is on Monday and English is on Tuesday, on which day can Science be scheduled? SOLUTION: Given:
Mathematics<English<Science \text{Mathematics}<\text{English}<\text{Science}
Therefore:
Monday<Tuesday<Science \text{Monday}<\text{Tuesday}<\text{Science}
The possible days for Science are Wednesday, Thursday or Friday. 🔵 ANSWER:
Wednesday, Thursday or Friday \text{Wednesday, Thursday or Friday}
🟢 EXAMPLE 15: IMMEDIATELY BEFORE QUESTION: Five subjects A, B, C, D and E are arranged from Monday to Friday. B is immediately after A. If A is on Tuesday, on which day is B? SOLUTION: B is immediately after A.
AB A\quad B
A is on Tuesday.
A=Tuesday \text{A}=\text{Tuesday}
Therefore:
B=Wednesday \text{B}=\text{Wednesday}
🔵 ANSWER:
Wednesday \text{Wednesday}
🟢 EXAMPLE 16: FIXED EXTREME POSITIONS QUESTION: Five people A, B, C, D and E stand in a row. A is at the extreme left and E is at the extreme right. Who can occupy the middle position? SOLUTION: The arrangement begins:
A___E A\quad\_\quad\_\quad\_\quad E
The remaining people are:
B, C, D B,\ C,\ D
The middle position is position 3. Therefore, any of B, C or D can occupy the middle position unless further conditions are given. 🔵 ANSWER:
B, C, or D B,\ C,\text{ or }D
🟢 EXAMPLE 17: ADJACENT PEOPLE QUESTION: A, B, C and D are standing in a row. A and B must stand together. How many possible orders can the four people have? SOLUTION: Treat A and B as one block.
(AB), C, D (AB),\ C,\ D
There are 3 units. The number of arrangements of the 3 units is:
3!=6 3!=6
Within the AB block, A and B can be arranged in:
2!=2 2!=2
Therefore:
Total Arrangements=3!×2! \text{Total Arrangements} = 3!\times2!
=6×2 =6\times2
=12 =12
🔵 ANSWER:
12 12
🟢 EXAMPLE 18: CIRCULAR ARRANGEMENT QUESTION: Four people A, B, C and D sit around a circular table. A sits immediately clockwise from B. If B is fixed at the top, where can A sit? SOLUTION: Since A is immediately clockwise from B:
B→A B\rightarrow A
Therefore, A occupies the position immediately clockwise from B. 🔵 ANSWER:
A sits immediately clockwise from B \text{A sits immediately clockwise from B}
🟢 EXAMPLE 19: FACING THE CENTRE QUESTION: Four people A, B, C and D sit around a circle facing the centre. A is immediately to the left of B. In which direction is A from B? SOLUTION: For people facing the centre:
Left=Clockwise \text{Left}= \text{Clockwise}
Therefore:
A is clockwise from B A\text{ is clockwise from }B
🔵 ANSWER:
Clockwise \text{Clockwise}
🟢 EXAMPLE 20: FACING OUTSIDE QUESTION: Four people A, B, C and D sit around a circle facing outside. A is immediately to the left of B. In which direction is A from B? SOLUTION: For people facing outside:
Left=Anticlockwise \text{Left}=\text{Anticlockwise}
Therefore:
A is anticlockwise from B A\text{ is anticlockwise from }B
🔵 ANSWER:
Anticlockwise \text{Anticlockwise}
🟢 EXAMPLE 21: POSITION FROM OPPOSITE SIDE QUESTION: There are 50 people in a queue. Ravi is 18th from the front. Find his position from the back. SOLUTION:
Position from Back=50−18+1 \text{Position from Back} = 50-18+1
=33 =33
🔵 ANSWER:
33rd from the back 33\text{rd from the back}
🟢 EXAMPLE 22: FINDING TOTAL PEOPLE QUESTION: A person is 14th from the left and 22nd from the right in a row. Find the total number of people. SOLUTION:
Total People=14+22−1 \text{Total People} = 14+22-1
=35 =35
🔵 ANSWER:
35 people 35\text{ people}
🟢 EXAMPLE 23: PERSON BETWEEN TWO PEOPLE QUESTION: A is 7th from the left and B is 15th from the left. C is exactly between A and B. Find the position of C. SOLUTION: The positions are:
7_______15 7\quad\_\quad\_\quad\_\quad\_\quad\_\quad\_\quad\_\quad15
The middle position is:
7+152 \frac{7+15}{2}
=222 =\frac{22}{2}
=11 =11
🔵 ANSWER:
C is in the 11th position C\text{ is in the }11\text{th position}
🟢 EXAMPLE 24: DATA ARRANGEMENT WITH CONDITIONS QUESTION: Five people A, B, C, D and E stand in a row. A is to the left of B. C is immediately to the right of B. D is at the extreme right. Find the arrangement. SOLUTION: Given:
A<B A<B
C is immediately right of B:
BC B\quad C
D is at the extreme right:
D=Last Position D=\text{Last Position}
Therefore:
ABCED A\quad B\quad C\quad E\quad D
🔵 ANSWER:
ABCED A\quad B\quad C\quad E\quad D
🟢 EXAMPLE 25: MIXED DATA ARRANGEMENT QUESTION: Six people P, Q, R, S, T and U stand in a row. P is at the extreme left. U is at the extreme right. Q is immediately to the right of P. R is immediately to the left of S. Find the arrangement. SOLUTION: P is at the extreme left:
P____U P\quad\_\quad\_\quad\_\quad\_\quad U
Q is immediately right of P:
PQ___U P\quad Q\quad\_\quad\_\quad\_\quad U
R is immediately left of S:
RS R\quad S
The remaining positions are 3 and 4. Therefore:
PQRSTU P\quad Q\quad R\quad S\quad T\quad U
🔵 ANSWER:
PQRSTU P\quad Q\quad R\quad S\quad T\quad U
🟢 EXAMPLE 26: ORDERING BY WEIGHT QUESTION: A is heavier than B. C is lighter than D. B is heavier than D. Arrange A, B, D and C from heaviest to lightest. SOLUTION: Given:
A>B A>B
B>D B>D
D>C D>C
Therefore:
A>B>D>C A>B>D>C
🔵 ANSWER:
A>B>D>C A>B>D>C
🟢 EXAMPLE 27: SCHEDULING QUESTION: Four exams Mathematics, English, Science and History are held from Monday to Thursday. Mathematics is before Science. English is after History. History is on Monday and Mathematics is on Tuesday. Find the schedule. SOLUTION: History is on Monday:
Monday=History \text{Monday}=\text{History}
Mathematics is on Tuesday:
Tuesday=Mathematics \text{Tuesday}=\text{Mathematics}
Mathematics is before Science:
Tuesday<Science \text{Tuesday}<\text{Science}
Therefore:
Science=Wednesday \text{Science}=\text{Wednesday}
English is after History:
English=Thursday \text{English}=\text{Thursday}
Therefore:
Monday=History \text{Monday}=\text{History}
Tuesday=Mathematics \text{Tuesday}=\text{Mathematics}
Wednesday=Science \text{Wednesday}=\text{Science}
Thursday=English \text{Thursday}=\text{English}
🔵 ANSWER:
Monday: History \text{Monday: History}
Tuesday: Mathematics \text{Tuesday: Mathematics}
Wednesday: Science \text{Wednesday: Science}
Thursday: English \text{Thursday: English}
🟢 EXAMPLE 28: NUMBER OF PEOPLE BETWEEN TWO RANKS QUESTION: In a class, Anu ranks 8th from the top and 17th from the bottom. How many students are between Anu and the top-ranked student? SOLUTION: Anu is:
8th from the top 8\text{th from the top}
The first-ranked student is:
1st from the top 1\text{st from the top}
Therefore:
8−1 8-1
=7 =7
🔵 ANSWER:
7 students 7\text{ students}
🟢 EXAMPLE 29: FINDING POSITION AFTER MOVEMENT QUESTION: A person is standing 12th from the left. If there are 5 people to his left who move to the right of him, what is his new position from the left? SOLUTION: Initially:
Position=12 \text{Position}=12
Five people move from his left to his right. Therefore, his position moves 5 places toward the left:
12−5 12-5
=7 =7
🔵 ANSWER:
7th from the left 7\text{th from the left}
🟢 EXAMPLE 30: MIXED RANKING PROBLEM QUESTION: In a queue, Ravi is 11th from the front. After 4 people ahead of Ravi leave the queue, what will be his new position from the front? SOLUTION: Initial position:
11 11
People ahead who leave:
4 4
New position:
11−4 11-4
=7 =7
🔵 ANSWER:
7th from the front 7\text{th from the front}