UPSC Prelims 2009 Q107: Science & Technology – Logical Reasoning & Puzzles
There are three cans A, B and
C. The capacities of A, B and C are 6 litres, 10 litres and 16 litres respectively. The can C contains
16 litres of milk. The milk has to be divided in them using these three cans only.
Consider the following statements :
1. It is possible to have 6 litres of milk each in can A and can B.
2. It is possible to have 8 litres of milk each in can B and can C.
Which of the statements given above is/are correct ?
- (a) 1 only
- (b) 2 only
- (c) Both 1 and 2
- (d) Neither 1 nor 2
Answer: (c) Both 1 and 2
Explanation
A classic can-pouring milk puzzle
Three cans — A (6L), B (10L), C (16L, full of milk) — and we check whether specific milk distributions are achievable using only these three cans.
| Statement | Verdict | Reason |
|---|---|---|
| 1. 6 litres each in A and B (4 litres remaining in C) | Correct | By repeatedly pouring between the cans (e.g., filling A from C, then transferring/adjusting via B), it is achievable to end up with exactly 6L in A, 6L in B, and 4L left in C |
| 2. 8 litres each in B and C | Correct | Through a similar sequence of pours between the three cans, it is also achievable to reach 8L in B, 8L in C, with 0L remaining in A |
Why both are achievable:
| Point | Detail |
|---|---|
| Puzzle type | Classic three-container water/milk redistribution puzzle |
| Key idea | Using the differences in capacities (6, 10, 16), multiple valid pouring sequences exist to reach various target splits |
Answer: (c) Both 1 and 2.
Why each option is right or wrong
- (a) Incorrect. Statement 2 (8L each in B and C) is also achievable, so '1 only' is incomplete.
- (b) Incorrect. Statement 1 (6L each in A and B) is also achievable, so '2 only' is incomplete.
- (c) CORRECT. Both target distributions — 6L in A & B, and 8L in B & C — can be reached through valid pouring sequences among the three cans.
- (d) Incorrect. Since both statements are achievable, 'neither' is wrong.
Key point
Using cans of 6L, 10L, and 16L (full), both target distributions — 6L each in A and B, and 8L each in B and C — are achievable through valid sequences of pours among the three cans.
Remember
With cans of 6L, 10L, and 16L (full): both 6L-each-in-A&B and 8L-each-in-B&C distributions are achievable.
Common mistakes
- Assuming a can-pouring puzzle's target split is impossible without actually working through a valid sequence of pours.
- Not considering multiple intermediate steps that a solution might require.
- Underestimating how flexible three-container puzzles can be, given carefully chosen capacities.
Exam tip
Classic three-can/jug puzzles: before declaring a target split 'impossible,' try working out an actual pouring sequence — many seemingly tricky splits are achievable.
Sources
- Arun Sharma — How to Prepare for Logical Reasoning for the CAT (puzzles on measures and pouring)
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Puzzle Test)