Directions, blood relations and Venn diagrams: previous-year questions
56 real UPSC Prelims questions (2011–2026) with the official answer and a clear explanation. 11 of them came in the last five papers.
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P has a son and a daughter. S is the mother of T. S is R's spouse. Q and R are children of P. Then how is Q related to S?
Answer (d) & explanation
Q is the sister of S's husband (d). Step 1: S is T's mother, so S is a woman. S is R's spouse, so R is a man. Step 2: Q and R are P's children, and P has one son and one daughter. R is the son, so Q is the daughter. Step 3: Q is R's sister, and R is S's husband. So Q is the sister of the husband of S (her sister-in-law). Options (a), (b) and (c) give wrong relations.
Tip: in blood-relation puzzles, first fix genders from clues like "mother" and "spouse". Then draw a small family tree.
Answer as per the official UPSC answer key.
A person facing the East travels 4 km straight and then turns right and travels 3 km, then further turns left and travels 2 km and finally turns left and travels 3 km. The minimum distance between the final point and the initial point, and the direction in which the person is facing at the final point are, respectively
Answer (d) & explanation
He ends 6 km away, facing North (d). Step 1: trace the path. Facing East, he walks 4 km East. A right turn faces South: 3 km. A left turn faces East: 2 km. A left turn faces North: 3 km. Step 2: South 3 and North 3 cancel out. East total = 4 + 2 = 6 km. So he is 6 km east of the start. Step 3: his last walk was northward, so he is facing North. Option (b) has the right distance but the wrong direction. Options (a) and (c) add the distances wrongly.
Tip: track north-south and east-west separately; opposite moves cancel. The final facing direction is simply the direction of the last walk.
Answer as per the official UPSC answer key.
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: How is Q related to P?
Statement I: P has two sisters, R and S.
Statement II: R's father is the brother of Q.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (d) & explanation
Even both statements together are not enough (d). Step 1: statement I says P has two sisters, R and S. So R is P's sibling. Step 2: statement II says R's father is Q's brother. R's father is also P's father. So Q is a sibling of P's father. Step 3: Q could be P's uncle (if male) or aunt (if female). Q's gender is not given, so the exact relation cannot be fixed. Options (a), (b) and (c) fail.
Tip: in relation questions, check that the gender of the person asked about is known. "Brother of Q" tells us about the brother, not about Q.
Answer as per the official UPSC answer key.
P is the brother of Q and R. S is R's mother. T is P's father. How many of the following statements are definitely true ?
- I. S and T are a couple.
- II. Q is T's son.
- III. T is Q's father.
- IV. S is P's mother.
- V. R is T's daughter.
- VI. P is S's son.
Select the correct answer using the code given below:
Answer (c) & explanation
Only four statements are definitely true (c). Step 1: P is the brother of Q and R, so P, Q and R are siblings. S is R's mother, so S is mother of all three. T is P's father, so T is father of all three. Step 2: so I (S and T are a couple), III (T is Q's father), IV (S is P's mother) and VI (P is S's son; P is a brother, so male) are true. Step 3: II says Q is T's son, and V says R is T's daughter. The genders of Q and R are not given, so these are not certain. That makes four. Options (a), (b) and (d) miscount.
Tip: in blood-relation questions, never assume gender from a name or letter. Only words like brother, mother or son fix gender.
Answer as per the official UPSC answer key.
There are 7 places A, B, C, D, E, F, and G in a city connected by various roads AB, CD, DE, BF, EG. A is 6 km south of B. A is 10 km west of C. D is 5 km east of E. C is 6 km north of D. F is 9 km west of B. F is 12 km north of G. A person travels from D to F through these roads. What is the distance covered by the person?
Answer (c) & explanation
The distance covered is 31 km (c). Step 1: place A at (0, 0). B is 6 km north: (0, 6). C is 10 km east of A: (10, 0). D is 6 km south of C: (10, −6). E is 5 km west of D: (5, −6). F is 9 km west of B: (−9, 6). G is 12 km south of F: (−9, −6). Step 2: the roads are AB, CD, DE, BF and EG. From D, the only route to F is D → E → G → F. Step 3: DE = 5, EG = 5 − (−9) = 14, GF = 12. Total = 5 + 14 + 12 = 31 km. Options (a), (b) and (d) take routes that do not exist.
Tip: draw coordinates, then follow only the given roads, not straight lines.
Answer as per the official UPSC answer key.
A person walks 100 m straight from his house, turns left and walks 100 m, again turns left and walks 300 m, then turns right and walks 100 m to reach his office. In which direction does he walk initially from his house if his office is exactly in the North-East direction?
Answer (c) & explanation
He first walked South (c). Step 1: test the options. Suppose he starts walking South 100 m. A left turn while facing South points East: 100 m East. Another left points North: 300 m North. A right turn points East: 100 m East. Step 2: net movement: East = 100 + 100 = 200 m; North = 300 − 100 = 200 m. Step 3: equal East and North means exactly North-East. Options (a), (b) and (d) do not give equal East and North parts.
Tip: in direction questions, testing each option is often faster than working backwards. Remember: facing South, your left is East and your right is West.
'left' depends on the way he faces. Facing South, his left is East, not West.
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Answer as per the official UPSC answer key.
A person walks 100 m Westward, then turns left and walks 100 m. He then takes 225° turn clockwise. In which direction is he walking now?
Answer (d) & explanation
He is now walking North-East (d). Step 1: he walks West. A left turn while facing West points South. Step 2: now turn 225° clockwise from South: 90° brings him to West, 180° to North, and 45° more (total 225°) to North-East. Step 3: so he faces North-East. Options (a), (b) and (c) come from turning the wrong way or miscounting the angle.
Tip: break big turns into 90° steps plus a remainder. Clockwise goes N → E → S → W; anticlockwise goes N → W → S → E. A 45° step lands on the corner directions (NE, SE, SW, NW).
the distances walked do not matter; only the facing direction does.
Answer as per the official UPSC answer key.
Consider the following including the Question and the Statements :
There are 5 members A, B, C, D, E in a family.
Question : What is the relation of E to B?
Statement-1 : A and B are a married couple.
Statement-2 : D is the father of C.
Statement-3 : E is D's son.
Statement-4 : A and C are sisters.
Which one of the following is correct in respect of the above Question and Statements?
Answer (c) & explanation
All four statements together are sufficient (c). Step 1: statements 2 and 4: D is C's father, and A is C's sister. So D is A's father too. Step 2: statement 3: E is D's son, so E is A's brother. Step 3: statement 1: B is married to A. So E is B's brother-in-law. Each statement is needed: without 2 or 4 we cannot link A to D; without 3 we know nothing of E; without 1 we know nothing of B. Options (a), (b) and (d) fail.
Tip: build a small family tree as you read each statement. Then test each option by removing one statement.
Option (b) leaves out D being C's father, so A cannot be tied to D and E.
Answer as per the official UPSC answer key.
Two friends X and Y start running and they run together for 50 m in the same direction and reach a point. X turns right and runs 60 m, while Y turns left and runs 40 m. Then X turns left and runs 50 m and stops, while Y turns right and runs 50 m and then stops. How far are the two friends from each other now?
Answer (a) & explanation
They are 100 m apart (a). Step 1: say they first run 50 m North together. Step 2: X turns right (East) and runs 60 m. Y turns left (West) and runs 40 m. Now they are 60 + 40 = 100 m apart on an east-west line. Step 3: X turns left (North) and runs 50 m. Y turns right (also North) and runs 50 m. Both move the same distance in the same direction, so the gap stays 100 m. Options (b), (c) and (d) miss this.
Tip: draw a quick sketch. When two people move the same distance in the same direction, the distance between them does not change.
the first 50 m and the last 50 m are common to both, so ignore them.
Answer as per the official UPSC answer key.
Consider the Question and two Statements given below :
Question : Is Z brother of X?
Statement-1 : X is a brother of Y and Y is a brother of Z.
Statement-2 : X, Y and Z are siblings.
Which one of the following is correct in respect of the Question and the Statements?
Answer (d) & explanation
Even both statements together are not enough (d). Step 1: Statement-1 says X is a brother of Y and Y is a brother of Z. So X and Y are male. Step 2: Statement-2 says all three are siblings, which we already know. Step 3: neither statement tells us Z's gender. Z could be X's brother or sister. So the question cannot be answered. Options (a), (b) and (c) fail.
Tip: in relation questions, "brother of Z" tells you the speaker's gender, not Z's. Always check if the gender of the person asked about is given.
'Y is a brother of Z' tells you Y's gender, not Z's.
Answer as per the official UPSC answer key.
P, Q, R, S, T and U are six members of a family. R is the spouse of Q. U is the mother of T and S is the daughter of U. P's daughter is T and R's son is P. There are two couples in the family. Which one of the following is correct?
No official answer (question dropped) & notes
UPSC dropped this question, so it has no official answer. Step 1: R is married to Q, and R's son is P. So P is the child of the couple Q and R. Step 2: P's daughter is T. So T is the granddaughter of Q (and of R). That matches option (d). Step 3: the genders of Q and R are never given. So "grandfather" (a), "grandmother" (b) and "R is the mother" (c) cannot be fixed. The wording about "two couples" adds more doubt, which is a likely reason UPSC dropped it.
Tip: in family puzzles, mark genders only when the question states them. Practise it, but don't overthink dropped items.
UPSC dropped this question from evaluation, so it has no official answer. It is printed here for practice only.
UPSC dropped this question from evaluation; there is no official answer.
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
Answer (b) & explanation
The shortest distance is 25 km (b). Step 1: trace the path. South 10 km. Facing South, left is East: 20 km. Facing East, left is North: 40 km. Facing North, right is East: 5 km. Facing East, right is South: 30 km. Step 2: north-south: −10 + 40 − 30 = 0. She ends on the same level as her house. East: 20 + 5 = 25 km. Step 3: so the bank is 25 km due East of the house. Options (a), (c) and (d) fail.
Tip: add up all north-south moves and all east-west moves separately. If one adds to zero, the answer is simply the other total.
Answer as per the official UPSC answer key.
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
Answer (b) & explanation
She is at an angle less than 45° North of East (b). Step 1: 12 km North, then 6 km South, leaves her 6 km North. Then 8 km East. Step 2: so her net position is 6 km North and 8 km East. Step 3: the north part (6) is less than the east part (8). So the direction is closer to East: tan θ = 6/8, giving about 37° North of East, less than 45°. Options (a) and (c) wrongly say South. Option (d) says more than 45°.
Tip: if the two parts are equal, the angle is exactly 45°. The bigger part decides which direction the line leans towards.
Answer as per the official UPSC answer key.
In a group of 120 persons, 80 are Indians and rest are foreigners. Further, 70 persons in the group can speak English. The number of Indians who can speak English is
Answer (d) & explanation
The number of Indians who speak English is 30 or more (d). Step 1: there are 120 people: 80 Indians and 40 foreigners. Step 2: 70 people speak English. Even if all 40 foreigners speak English, at least 70 − 40 = 30 speakers must be Indian. Step 3: if fewer foreigners speak English, more Indians must. It can go up to all 70. So the answer is "30 or more". Option (a), exactly 20, is impossible, and option (b), exactly 30, is only the least case. Option (c), 30 or less, gets the direction wrong.
Tip: for "at least" questions, give the other group the most it can take. What is left is the minimum for your group.
the question asks for what must be true. Find the smallest overlap, not an exact number.
Answer as per the official UPSC answer key.
A family of two generations consisting of six members P, Q, R, S, T and U has three males and three females. There are two married couples and two unmarried siblings. U is P's daughter and Q is R's mother-in-law. T is an unmarried male and S is a male. Which one of the following is correct?
Answer (b) & explanation
R is S's wife (b). Step 1: Q is R's mother-in-law. So Q is in the older generation, and R married Q's child. Step 2: the two unmarried siblings must be T (unmarried male) and U (P's daughter). So R's spouse is the remaining child, S, a male. The couples are P–Q and S–R. Step 3: males: P, S, T. Females: Q, R, U. So R is S's wife. Option (a) fails because U is unmarried. Option (c) fails because S is married. So (d) fails too.
Tip: in family puzzles, first count generations and couples. Then place unmarried people; the married pairs follow.
Answer as per the official UPSC answer key.
A man walks down the backside of his house straight 25 metres, then turns to the right and walks 50 metres again; then he turns towards left and again walks 25 metres. If his house faces to the East, what is his direction from the starting point?
Answer (d) & explanation
He is North-West of his starting point (d). Step 1: the house faces East, so its back side faces West. He walks 25 m West. Step 2: facing West, a right turn points him North. He walks 50 m North. Facing North, a left turn points him West. He walks 25 m West. Step 3: net movement: 25 + 25 = 50 m West and 50 m North. Equal amounts of West and North give North-West. Options (a), (b) and (c) fail.
Tip: draw a quick sketch with N at the top. Remember: facing West, right is North and left is South. Equal moves in two directions give the in-between direction.
Answer as per the official UPSC answer key.
In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct ?
- 1. At least 30 Indian participants are vegetarian.
- 2. At least 10 Indian participants are non-vegetarian.
Select the correct answer using the code given below :
Answer (c) & explanation
Both statements are correct (c). Step 1: the smallest possible overlap of two groups = group A + group B − total. Step 2: Indians and vegetarians: 70 + 60 − 100 = 30. So at least 30 Indians are vegetarian. Statement 1 holds. Step 3: there are 100 − 60 = 40 non-vegetarians. Indians and non-vegetarians: 70 + 40 − 100 = 10. So at least 10 Indians are non-vegetarian. Statement 2 holds. Options (a), (b) and (d) fail.
Tip: remember minimum overlap = A + B − total. Picture it: even if all 30 non-Indians are vegetarian, 30 more vegetarians must be Indian.
Answer as per the official UPSC answer key.
P, Q and R are three towns. The distance between P and Q is 60 km, whereas the distance between P and R is 80 km. Q is in the West of P and R is in the South of P. What is the distance between Q and R ?
Answer (d) & explanation
The distance between Q and R is 100 km (d). Step 1: Q is west of P and R is south of P. West and south are at right angles, so P is the right-angle corner of a triangle. Step 2: by Pythagoras, QR² = 60² + 80² = 3600 + 6400 = 10,000. Step 3: so QR = √10,000 = 100 km. Option (a), 140 km, simply adds 60 and 80, which would be true only if you travelled via P. Options (b) and (c) do not fit.
Tip: 60-80-100 is the 3-4-5 triangle multiplied by 20. Spotting such triples saves calculation. Direction questions with north-south and east-west legs almost always use Pythagoras.
Answer as per the official UPSC answer key.
All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data ?
- 1. 40% members went for shopping as well as sightseeing.
- 2. 20% members went for only shopping.
Select the correct answer using the code given below :
Answer (a) & explanation
Only conclusion 1 can be drawn (a). Step 1: 10% stayed in the hotel, so 90% went out. Step 2: both shopping and sightseeing = 80 + 50 − 90 = 40%. So conclusion 1 is correct. Step 3: only shopping = all shoppers − those who did both = 80 − 40 = 40%, not 20%. So conclusion 2 is wrong. Options (b), (c) and (d) fail.
Tip: always remove the "neither" group first. Then use: both = A + B − (those in at least one). A quick two-circle diagram makes "only A" and "both" easy to read off. Option (b) traps those who subtract 80 from 100 to get 20%.
Answer as per the official UPSC answer key.
In a group of 15 people, 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is
Answer (b) & explanation
9 people can read exactly one language (b). Step 1: 3 read neither, so 15 − 3 = 12 read at least one. Step 2: both = 7 + 8 − 12 = 3. Step 3: exactly one = those who read at least one − those who read both = 12 − 3 = 9. Check: French only = 7 − 3 = 4; English only = 8 − 3 = 5; 4 + 5 = 9. Option (a), 10, forgets to subtract correctly. Option (c), 5, and (d), 4, give only one language's "only" group.
Tip: "exactly one" = (A only) + (B only). Always remove the "neither" group before using the overlap formula.
Answer as per the official UPSC answer key.