Overview: Ranking Test | CSAT Preparation - UPSC PDF Download

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Questions from this topic are asked almost every year. So, this chapter is very important in context to CSAT exam.

Mostly questions asked from this chapter are based on comparison of persons/objects on the basis of age, height, weight, marks, position in a row, etc.

In the year 2023, one question and in 2022 one question was asked from this chapter. In previous years, one to five questions have typically appeared from this chapter.

Practice of this chapter is must for every aspirant in the context of CSAT exam.

Ranking Test

Ranking problems require comparison among a group of items (persons, objects, scores, dates, etc.) to determine order - ascending or descending - according to the attribute specified. Questions supply partial relations or positions and expect you to deduce complete order or specific ranks using logical deductions and simple arithmetic relationships.

Types of Ranking

• Fixed ranking: The position of each object/person is definite and can be determined uniquely from the information given.
• Variable ranking: The position of one or more objects/persons cannot be determined uniquely from the given information; their ranks may vary depending on remaining possibilities.

Methodology to Solve the Questions

When information is complicated or scattered, establish pairwise relationships and combine them into a single ordering. Use the symbols > (greater than), < (less than), = (equal), ≥ (greater than or equal to) and ≤ (less than or equal to) to record relations. Convert positional information (from left/right, front/back, top/bottom) into numerical relationships using the formulas given below. Work step-by-step, keep a clear diagram or a short list of relations, and check consistency.

Illustration 1

Roshan is taller than Hardik who is shorter than Susheel. Niza is taller than Harry but shorter than Hardik. If Susheel is shorter than Roshan, then who is the tallest? (a) Roshan (b) Susheel (c) Hardik (d) Harry

Sol: (a)

From the statements, record pairwise relations:

• Roshan > Hardik
• Susheel > Hardik
• Niza > Harry
• Hardik > Niza
• Roshan > Susheel

Combine the relations to get the final descending order of height:

Roshan > Susheel > Hardik > Niza > Harry

Hence, the tallest person is Roshan.

Formulas for Order and Ranking

• Finding a rank from the other end: Required rank = Total - (given rank - 1)
• Finding total when rank from both ends is known: Total = (rank from left) + (rank from right) - 1
• Finding total number when ranks of two persons and number of persons between them are given (simple non-overlapping case):
  1. Total = (R1 + R2) + number of middle persons
• Overlapping case (when given ranks overlap):
  1. Total = (R1 + R2) - (number of middle persons + 2)
  2. Apply this only when the given ranks indicate overlap; check diagrammatically before using.
• Number of persons between two given persons (simple case): Number between = Total - (Rank from left + Rank from right)
• Number of persons between two given persons (overlapping case): Number between = (Rank from left + Rank from right) - (Total + 2)
• Finding rank of middle person (quick trick):
  1. Convert both ranks to the same side (the side from which the middle rank is to be found).
  2. Take the average of those two ranks - that gives the middle person's rank.
• Shortcut for calculating maximum and minimum persons in a row: Use standard diagrams to visualise middle positions and symmetry; keep mid-number (number of middle persons) in mind when computing extremes.

Note: Mid no. refers to number of the middle persons when the row has even number of persons there are two middle positions; for odd number there is a single exact middle.

Solved Examples

Example 1: In a queue, Vijay is fourteenth from the front and Jack is seventeenth from the end, while Mary is exactly at the middle of Vijay and Jack. If Vijay be ahead of Jack and there be 48 persons in the queue, how many persons are there between Vijay and Mary? (a) 5 (b) 6 (c) 7 (d) 8 (e) None of these Ans: (d)

Explanation:

Number of persons between Vijay and Jack = 48 - (14 + 17) = 17.

Mary lies exactly in the middle of these 17 persons, so Mary's position among these is the 9th.

Number of persons between Vijay and Mary = 9 - 1 = 8.

Example 2: Kunal ranked sixteenth from the top and twenty ninth from the bottom among those who passed an examination. Six boys did not participate in the competition and five failed in it. How many boys were there in the class? (a) 35 (b) 45 (c) 50 (d) 55 (e) None of these Ans: (d)

Explanation:

Number of boys who passed = (16 - 1) + 1 + (29 - 1) = 15 + 1 + 28 = 44.

Total number of boys in the class = number who passed + those who did not participate + those who failed.

Total = 44 + 6 + 5 = 55.

Example 3: In a queue of children, Ajay is fifth from the left and Sunil is sixth from the right. When they interchange their places among themselves, Ajay becomes thirteenth from the left. Then, what will be Sunil's position from the right? (a) 8th (b) 14th (c) 15th (d) 16th (e) None of these Ans: (b)

Explanation:

After interchange, Ajay's new position (13th from left) equals Sunil's earlier position (6th from right).

Therefore, total number of children = 13 + 5 = 18.

Now, after interchange Sunil takes Ajay's earlier place (5th from left).

Sunil's position from the right = 18 - (5 - 1) = 18 - 4 = 14th.

Example 4: Students line up in a queue in which Aman stands fifteenth from the left and Simran is seventh from the right. If they interchange their places, Simran would be fifteenth from the right. How many students are there in the queue? (a) 21 (b) 22 (c) 28 (d) 29 (e) None of these Ans: (d)

Explanation:

Simran after interchange becomes 15th from the right; that position corresponds to 15th from the left as well (because Aman becomes seventh from right earlier and positions swap symmetrically).

Therefore total students = (15 - 1) + 1 + (15 - 1) = 14 + 1 + 14 = 29.

Example 5: Ram is 27th place from left end in the row of 44 boys. Rohit is 15th from the right end in the same row. How many boys are there between them in the row? (a) Eleven (b) Ten (c) Six (d) Two (e) None of these Ans: (d)

Explanation:

Total boys between them = 44 - (27 + 15) = 44 - 42 = 2.

Example 6: In a row of girls, Rita and Monika occupy the ninth place from the right end and tenth place from the left end, respectively. If they interchange their places, then Rita and Monika occupy seventeenth place from the right and eighteenth place from the left respectively. How many girls are there in the row? (a) 25 (b) 26 (c) 27 (d) Data inadequate (e) None of these Ans: (b)

Explanation:

Given after interchange Rita is 17th from the right. The corresponding position from the left is (Total - 17 + 1).

But Monika after interchange is 18th from the left; these correspond to the same positions, so Total = 17 + 9 = 26.

Example 7: Jai is 25th from left and Vijay is 24th from right. When they interchange their positions respectively then Vijay becomes 31st from right end. What will be Jai's position from left after interchanging? (a) 25 (b) 26 (c) 27 (d) 28 (e) None of these Ans: (e)

Explanation:

Vijay after interchange becomes 31st from right; that means the original position corresponding yields an offset of 6 places (31 - 25 = 6) relative to Jai's original left position.

Therefore Jai's position from the left after interchanging = 25 + 6 + 1 = 32.

Example 8: Zombo, correctly remembers that his father's birthday is before 29th July but after 24th July whereas his younger brother correctly remembers that their father's birthday is after 23rd July but before 28th July and his elder brother correctly remembers that their father's birthday is on an odd date. On which date of July is definitely their father's birthday? (a) Twenty-five or Twenty-seven (b) Twenty-seven (c) Twenty-five (d) Twenty-six (e) None of these Ans: (a)

Explanation:

Combine the ranges: father's birthday is after 24th and before 29th ⇒ possible dates: 25, 26, 27, 28.

Younger brother's memory restricts to after 23rd and before 28th ⇒ possible dates: 24, 25, 26, 27.

Intersection of both ranges = 25, 26, 27.

Elder brother remembers it is an odd date ⇒ possible odd dates in intersection = 25, 27.

Therefore the father's birthday is definitely either 25th or 27th July.

Example 9: Among Zojo, Yo, Xe, William and Vicky each scoring different marks in a test. Xe scored more than William but not as much as Vicky. Vicky scored more than Zojo, who scored less than Yo. Who did score second highest marks? (a) Yo (b) Zojo (c) Xe (d) Data inadequate (e) None of these Ans: (d)

Explanation:

From the given relations: Xe > William Vicky > Xe Vicky > Zojo Yo > Zojo

These do not fix the relative order between Yo, Vicky and Xe completely; Yo could be highest or second highest depending on unprovided comparisons. Therefore data is inadequate to determine the definite second highest scorer.

Example 10: In a row of 40 girls, when Komal was shifted to her left by 4 places her number from the left end of the row became 10. What was the place of Swati from the right end of the row if Swati was three places to the right of Komal's original position? (a) 22 (b) 23 (c) 25 (d) 26 (e) None of these Ans: (e)

Explanation:

After shifting Komal 4 places to the left she becomes 10th from the left.

Therefore Komal's original position from the left = 10 + 4 = 14th.

Swati is 3 places to the right of Komal's original position, so Swati's position from the left = 14 + 3 = 17th.

Number of girls to the right of Swati = 40 - 17 = 23.

So Swati's position from the right = 23 + 1 = 24th.

Final notes for practice:

• Always draw a short linear diagram (row, column, vertical list) for positional and ranking problems - it reduces errors.
• Translate "from left" / "from right" and "from front" / "from back" consistently using the formula Total - (rank - 1) when converting sides.
• Check for overlapping cases where ranks given imply the same segment of the row - treat overlap carefully using the overlapping formulas.
• For comparative puzzles (height/weight/marks), list direct pairwise inequalities and combine them; look for transitive chains to get complete order or detect ambiguity.