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?
Solving the Friends' Height Comparison
This problem involves comparing the heights of five friends based on the given clues to determine who is the tallest.
Understanding the Height Relationships
We are given the following information about the heights of Prakash, Qadir, Ramesh, Saurabh, and Tariq:
- Ramesh is taller than Qadir. We can write this as: Ramesh > Qadir.
- Ramesh is shorter than Saurabh. This means Saurabh is taller than Ramesh. We can write this as: Saurabh > Ramesh.
- Prakash is the shortest among all five friends.
- Tariq is taller than Saurabh. We can write this as: Tariq > Saurabh.
Combining the Information to Find the Tallest Friend
Let's combine the height comparisons step-by-step:
- From the first two points, we have Saurabh > Ramesh and Ramesh > Qadir. This means Saurabh is also taller than Qadir. We can string these together: Saurabh > Ramesh > Qadir.
- We are told that Tariq is taller than Saurabh: Tariq > Saurabh.
- Combining this with the previous step, we get: Tariq > Saurabh > Ramesh > Qadir.
- Finally, we know Prakash is the shortest. So, Prakash is shorter than Qadir, Ramesh, Saurabh, and Tariq.
Putting it all together, the order of heights from tallest to shortest is:
Tariq > Saurabh > Ramesh > Qadir > Prakash
Using mathematical notation for height, let $H_X$ be the height of person $X$:
- $H_{\text{Ramesh}} > H_{\text{Qadir}}$
- $H_{\text{Saurabh}} > H_{\text{Ramesh}}$
- $H_{\text{Tariq}} > H_{\text{Saurabh}}$
- $H_{\text{Prakash}}$ is the minimum height.
From these inequalities, we can deduce the order:
- $H_{\text{Tariq}} > H_{\text{Saurabh}}$
- $H_{\text{Saurabh}} > H_{\text{Ramesh}}$
- $H_{\text{Ramesh}} > H_{\text{Qadir}}$
- $H_{\text{Qadir}} > H_{\text{Prakash}}$ (since Prakash is the shortest)
Thus, the complete order from tallest to shortest is:
$H_{\text{Tariq}} > H_{\text{Saurabh}} > H_{\text{Ramesh}} > H_{\text{Qadir}} > H_{\text{Prakash}}$
Based on this order, the person with the maximum height is Tariq.
| Friend | Height Comparison |
|---|---|
| Prakash | Shortest |
| Qadir | Shorter than Ramesh |
| Ramesh | Taller than Qadir, Shorter than Saurabh |
| Saurabh | Taller than Ramesh, Shorter than Tariq |
| Tariq | Tallest (Taller than Saurabh) |
Conclusion: Who is the Tallest?
By analyzing the given clues and establishing the height order, we can clearly see that Tariq is taller than everyone else mentioned.
Therefore, Tariq is the tallest among them.
Revision Table: Height Comparison Summary
| Relationship | Inequality |
|---|---|
| Ramesh is taller than Qadir | Ramesh > Qadir |
| Ramesh is shorter than Saurabh | Saurabh > Ramesh |
| Tariq is taller than Saurabh | Tariq > Saurabh |
| Prakash is the shortest | Prakash < All others |
| Combined Order (Tallest to Shortest) | Tariq > Saurabh > Ramesh > Qadir > Prakash |
Additional Information: Logical Reasoning and Ordering Problems
This type of question is a common example of a logical reasoning problem, specifically an ordering or ranking problem. These problems require you to deduce the relative positions or ranks of items or people based on a set of comparative statements.
Key strategies for solving such problems include:
- Identifying the elements being compared (in this case, friends).
- Identifying the attribute being compared (in this case, height).
- Representing the relationships using symbols (like >, <, or =).
- Combining the individual relationships to form a complete or partial order.
- Drawing a diagram or writing down the inequalities can help visualize the relationships and avoid confusion.
Mastering ordering problems improves analytical skills and is useful in various standardized tests and real-life situations requiring deductive reasoning.
Important Questions from Order Based
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?
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?
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?
Seven chocolates A, B, C, D, E, F and G are bought at different costs between Rs. 40 and Rs. 50 (excluding 40 and 50) but not necessarily in the same order. The cost of chocolate C is five less than that of chocolate E. The cost of the chocolate A is a prime number. The cost of chocolate F is two more than that of chocolate A. The cost of chocolate F is more than that of chocolate E. The cost of chocolate D is an odd number. The cost of chocolate G is three more than the cost of chocolate D. None of the chocolates costs Rs. 44. The cost of chocolate B is an even number. Which is the following chocolates is costlier than E?
