Pinky is taller than Priya but shorter than Reena. Riya is taller than Sheela, who is shorter than Priya. Reena is taller than Riya, who is taller than Pinky. Who is the shortest?
Sheela
Understanding Height Comparison Problems
This question involves comparing the heights of five individuals: Pinky, Priya, Reena, Riya, and Sheela, based on a set of given relationships. To find the shortest person, we need to arrange them in order of height by combining these relationships.
Analyzing the Given Height Relationships
Let's list the given statements about their relative heights:
- Pinky is taller than Priya. (Pinky > Priya)
- Pinky is shorter than Reena. (Reena > Pinky)
- Riya is taller than Sheela. (Riya > Sheela)
- Sheela is shorter than Priya. (Priya > Sheela)
- Reena is taller than Riya. (Reena > Riya)
- Riya is taller than Pinky. (Riya > Pinky)
Deducing the Height Order
We can combine these statements to establish a clear order from tallest to shortest.
- From "Pinky > Priya" and "Priya > Sheela", we know that Pinky is taller than Priya, who is taller than Sheela. This gives us the sequence: Pinky > Priya > Sheela.
- From "Riya > Pinky", we know Riya is taller than Pinky. Combining this with the previous sequence (Pinky > Priya > Sheela), we get: Riya > Pinky > Priya > Sheela.
- From "Reena > Riya", we know Reena is taller than Riya. Combining this with the sequence from step 2 (Riya > Pinky > Priya > Sheela), we get the complete order: Reena > Riya > Pinky > Priya > Sheela.
Let's verify this final order against all original statements:
- Pinky > Priya? Yes (Pinky is to the left of Priya).
- Reena > Pinky? Yes (Reena is to the left of Pinky).
- Riya > Sheela? Yes (Riya is to the left of Sheela).
- Priya > Sheela? Yes (Priya is to the left of Sheela).
- Reena > Riya? Yes (Reena is to the left of Riya).
- Riya > Pinky? Yes (Riya is to the left of Pinky).
All statements are consistent with the order: Reena > Riya > Pinky > Priya > Sheela.
Identifying the Shortest Person
In the deduced height order Reena > Riya > Pinky > Priya > Sheela, the person on the far right is the shortest. Therefore, Sheela is the shortest.
| Individual | Relative Height |
|---|---|
| Reena | Tallest |
| Riya | Taller than Pinky, Priya, Sheela; Shorter than Reena |
| Pinky | Taller than Priya, Sheela; Shorter than Reena, Riya |
| Priya | Taller than Sheela; Shorter than Pinky, Riya, Reena |
| Sheela | Shortest |
Based on the complete height ranking, Sheela is the shortest among the five individuals.
Revision Table: Key Concepts
| Concept | Description |
|---|---|
| Relative Comparison | Determining order based on comparisons (taller than, shorter than). |
| Transitivity | If A > B and B > C, then A > C. Used to chain comparisons. |
| Deduction | Using given facts to logically arrive at a conclusion (the height order). |
Additional Information: Solving Comparison Problems
Comparison problems like this are common in logical reasoning. The key is to translate the verbal statements into symbolic relationships (>, <) and then combine these relationships step-by-step to form a single, consistent sequence or order. Sometimes, drawing a diagram or writing the names in order as you deduce the relationships can be helpful. Always double-check your final order against all the original statements to ensure consistency.
Important Questions from Order Based
Prakash, Qadir, Ramesh, Saurabh and Tariq are friends. Ramesh is taller than Qadir but shorter than Saurabh. Prakash is the shortest, and Tariq is taller than Saurabh. Who is the tallest among them?
Five friends, H, I, J, K and L, are top rank holders of a school. The rank of H is just above the rank of K and just below the rank of L. I is at the top rank and J is not at the lowest rank. Who among them is at the lowest rank?
Sonu is taller than Yatendra, Amit is taller than Sonu. Subhash is taller than Amit. Sattu is tallest of all. If they stand according to their height who will be exactly in the middle?
R is taller than T. Both P and Q are taller than S, whose height is between P and T. If S is taller than T, who is the shortest?
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