Question

Directions: A circular field, with inner radius of 10 meters and outer radius of 20 meters, was divided into five successive stages for ploughing. The ploughing of each stage was handed over to a different farmer.

1. Farmers are referred to by the symbols F1, F2, F3, F4, F5.
2. The points between different stages are referred to by the symbols P1, P2, P3, P4, P5, not necessarily in that order.
3. Farmer F5 was given the work of ploughing the stage starting at point P4.
4. The stage from point P5 to point P3 was not the first stage.
5. Farmer F4 was given the work of the fourth stage.
6. Stage 3 finished at point P1, and the work of which was not given to farmer F1.
7. Farmer F3 was given the work of the stage ending at point P5.

Which were the starting and finishing points for stage 2?

• A. P2 and P5
• B. P5 and P3
• C. P3 and P1
• D. P5 and P4

Hint:

Fix stage 3's finish point first using clue 6, then use clue 4 to place the P5-to-P3 stage, and use clues 3 and 7 to resolve the last two points.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Five farmers plough five successive stages of a circular field, one after another, so the finish point of one stage is the start point of the next. We are given seven clues about how the points P1 to P5 and the farmers F1 to F5 fit onto this five-stage loop, and we must find the start and finish points of stage 2.

Step 2: Key Formula or Approach:
Since the stages run one after another around the field, write the loop as X1 to X2 to X3 to X4 to X5 back to X1, where X1..X5 is some order of the points P1 to P5, and stage n runs from Xn to X(n+1). Use clue 6 to fix one point first, then clue 4 to place the "P5 to P3" stage, then clues 3, 5, and 7 to check which placement of the remaining points is consistent.

Step 3: Detailed Explanation:
Clue 6 says stage 3 finishes at P1, so X4 = P1.
Clue 4 says the "P5 to P3" stage is not stage 1. Testing it as stage 3 or stage 4 clashes with X4 = P1 (its start or finish would have to be P1, not P5 or P3), so it cannot sit there. Testing it as stage 5 also breaks down further along, because it then forces two different farmers onto the same stage once clues 3, 5, and 7 are applied.
So the "P5 to P3" stage must be stage 2, meaning X2 = P5 and X3 = P3.
With X2 = P5, X3 = P3, X4 = P1 fixed, only P2 and P4 remain for X1 and X5.
Clue 3 says F5's stage starts at P4. If X1 = P4, stage 1 (X1 to X2) would start at P4 and end at P5, so F5 would plough it, but clue 7 already sends the stage ending at P5 to farmer F3, a clash.
So X1 = P2 and X5 = P4 instead. The full loop becomes: stage 1 = P2 to P5, stage 2 = P5 to P3, stage 3 = P3 to P1, stage 4 = P1 to P4, stage 5 = P4 to P2.
Checking farmers: stage 5 starts at P4, so F5 ploughs stage 5 (clue 3). Stage 1 ends at P5, so F3 ploughs stage 1 (clue 7). F4 ploughs stage 4 (clue 5). Clue 6 keeps stage 3 away from F1, so F2 ploughs stage 3 and F1 ploughs stage 2. Every clue checks out.

Step 4: Final Answer:
Stage 2 runs from P5 to P3. \[ \boxed{\text{Stage 2: P5 to P3}} \]