Eight balls are placed on the floor at various distances and directions from each other. Determine the direction of ball R with respect to ball O.

**Statement I:** Ball R is 15 m west of ball P. Ball M is 6 m south of ball R. Ball T is 12 m north of ball Q.

**Statement II:** Ball S is 15 m south of ball P. Ball O is 6 m south of ball N. Ball T is 18 m west of ball O. Ball N is 9 m east of ball S.

Using the above information, find the direction of ball R from ball O.

Question

Eight balls are placed on the floor at various distances and directions from each other. Determine the direction of ball R with respect to ball O.

**Statement I:** Ball R is 15 m west of ball P. Ball M is 6 m south of ball R. Ball T is 12 m north of ball Q.

**Statement II:** Ball S is 15 m south of ball P. Ball O is 6 m south of ball N. Ball T is 18 m west of ball O. Ball N is 9 m east of ball S.

Using the above information, find the direction of ball R from ball O.

Accepted Answer

**Solution:**

1. From Statement I alone, we know the relative positions of balls R, P, M, T, and Q but have no information about ball O's position.

2. Statement II alone gives the relative positions of balls S, P, O, N, and T but does not mention ball R's position relative to O.

3. Combining both statements, we can place all balls relative to each other:
   - From Statement I: R is 15 m west of P, M is 6 m south of R.
   - From Statement II: S is 15 m south of P, O is 6 m south of N, T is 18 m west of O, N is 9 m east of S.

4. Using these, we can deduce the position of R relative to O. After plotting or logically combining the distances and directions, ball R lies to the north-west of ball O.

**Answer:** (e) If the data given in both the statements I and II together are necessary to answer

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