Practice Questions
Concept Explanation
Rank problems find position from left/right or count persons between positions. Total = left rank + right rank − 1.
Key Formulas
- Total persons = L + R − 1 (L = rank from left, R = rank from right)
- Persons between two at ranks a and b = |a − b| − 1
- Arrangements with fixed positions use nPr on remaining slots
Example
Rank 5 from left and 8 from right in a line: total = 5 + 8 − 1 = 12.
Common Trap
Do not add left and right ranks directly; subtract 1 for double counting the person.
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Q1 EasyA person is 5th from the left and 8th from the right in a row. How many persons are there in the row?ExplanationTotal persons = (rank from left) + (rank from right) − 1, because the person is counted twice. So total = 5 + 8 − 1 = 12. Hence the answer is 12.
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Q2 EasyIn a row of 15 persons, what is the rank from the right of the person who is 6th from the left?ExplanationRank from right = (total) − (rank from left) + 1 = 15 − 6 + 1 = 10. Hence the answer is 10.
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Q3 EasyHow many persons sit between the 4th from the left and the 9th from the left in the same row?ExplanationPersons between two left-ranks a and b = |a − b| − 1 = |9 − 4| − 1 = 4. Hence the answer is 4.
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Q4 EasyA person is 3rd from the left and 10th from the right. How many persons are in the row?ExplanationTotal = 3 + 10 − 1 = 12. Hence the answer is 12.
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Q5 MediumIf all the letters of the word RANK are arranged in all possible ways as in a dictionary, what is the rank of the word RANK?ExplanationLetters of RANK in alphabetical order: A, K, N, R. Words starting with A: 3! = 6; with K: 3! = 6; with N: 3! = 6. Words starting with RA and next letter before N: only RAK∗ = 2! = 2, of which RAKN comes before RANK. So arrangements before RANK = 6 + 6 + 6 + 1 = 19, and RANK itself is next. Rank = 19 + 1 = 20. Hence the answer is 20.
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Q6 MediumIn a row of 20, the person 8th from the left is how many from the right?ExplanationRank from right = 20 − 8 + 1 = 13. Hence the answer is 13.
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Q7 MediumIf all the letters of the word AGAIN are arranged as in a dictionary, what is the rank of the word AGAIN?ExplanationAGAIN has letters A, A, G, I, N. Words with first letter A and second letter A (before G): remaining G,I,N → 3! = 6 words of the form AA∗∗∗. Next comes AG∗∗∗. With AGA, remaining I,N give AGAIN and AGANI; AGAIN comes first among these. Arrangements before AGAIN = 6, so rank = 7. Hence the answer is 7.
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Q8 MediumA person is 12th from the left and also 12th from the right. How many persons are there?ExplanationTotal = 12 + 12 − 1 = 23. Hence the answer is 23.
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Q9 MediumIn a row of 11, how many persons sit between the 5th from the left and the 5th from the right?Explanation5th from the right = (11 − 5 + 1)th from the left = 7th from the left. Persons between 5th and 7th from left = 7 − 5 − 1 = 1. Hence the answer is 1.
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Q10 MediumIf all the letters of the word TAKE are arranged as in a dictionary, what is the rank of the word TAKE?ExplanationLetters of TAKE in order: A, E, K, T. Words starting with A: 3! = 6; with E: 3! = 6; with K: 3! = 6. Words starting with TA and next letter before K: only TAE∗ (1 arrangement TAEK) before TAKE. Arrangements before TAKE = 6 + 6 + 6 + 1 = 19, so rank = 20. Hence the answer is 20.
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Q11 MediumSix people sit in a row. A is 2nd from the left and B is 3rd from the right. How many persons sit between A and B?ExplanationA is at position 2 from left. B is 3rd from right ⇒ position from left = 6 − 3 + 1 = 4. Persons between positions 2 and 4 = 4 − 2 − 1 = 1. Hence the answer is 1.
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Q12 HardIf all the letters of the word SILVER are arranged as in a dictionary, what is the rank of the word SILVER?ExplanationLetters of SILVER in alphabetical order: E, I, L, R, S, V. Words starting with E, I, L, or R: 4 × 5! = 480. Words starting with SE (letter before I after S): 4! = 24. Words starting with SIE (letter before L after SI): 3! = 6. Words starting with SILE or SILR (letters before V after SIL): 2! + 2! = 4. Arrangements before SILVER = 480 + 24 + 6 + 4 = 514, so rank of SILVER = 515. Hence the answer is 515.
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Q13 HardIf all the letters of the word QUEUE are arranged in all possible manners as in a dictionary, then the rank of the word QUEUE is:ExplanationQUEUE has letters Q, U, E, U, E (E twice, U twice). Alphabetical order: E, E, Q, U, U. Words starting with E: remaining E,Q,U,U → 4!/(2!) = 12. Words starting with QE: remaining E,U,U → 3!/2! = 3. Words starting with QUE: remaining E,U → QUEEU then QUEUE, so 1 word (QUEEU) comes before QUEUE. Arrangements before QUEUE = 12 + 3 + 1 = 16, so rank = 17. Hence the answer is 17th.
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Q14 HardIf all the letters of the word LOGIN are arranged as in a dictionary, what is the rank of the word LOGIN?ExplanationLetters of LOGIN in alphabetical order: G, I, L, N, O. Words starting with G: 4! = 24; with I: 4! = 24. Words starting with LG, LI, or LN (letters before O after L): 3 × 3! = 18. Words starting with LO then a letter before G: none, since remaining letters G, I, N begin with G. Under LOG, LOGIN is the first arrangement (I before N). Arrangements before LOGIN = 24 + 24 + 18 = 66, so rank = 67. Hence the answer is 67.
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DS1 Easy
In a campus ranking drill, what is the total number of persons in the row?
Statement IA person is 5th from the left.
Statement IIThe same person is 8th from the right.
ExplanationStatement I alone gives only the left rank. Statement II alone gives only the right rank. Together: total = 5 + 8 − 1 = 12. Both are needed. Answer: C. -
DS2 Easy
An HR quiz asks for the rank from the right of a person in a row. What is that rank?
Statement IThere are 15 persons in the row.
Statement IIThe person is 6th from the left.
ExplanationNeed total and left rank together: right rank = 15 − 6 + 1 = 10. Answer: C.
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DS3 Medium
What is the rank of the word CAT among its arrangements?
Statement IThe letters C, A, T are all distinct.
Statement IIAll permutations of CAT are listed in alphabetical order.
ExplanationNeither statement alone names the target word’s position without both knowing the letters and that dictionary order is used. Together: arrangements are ACT, ATC, CAT, CTA, TAC, TCA, so CAT is 3rd. Both are needed. Answer: C. -
DS4 Medium
Whether the total number of persons exceeds 20.
Statement IA person’s rank from the left is 11.
Statement IIThe same person’s rank from the right is 11.
ExplanationEach statement alone is insufficient. Together: total = 11 + 11 − 1 = 21 > 20. Both are needed. Answer: C.