The weight of Sona is four times that of Mona. The weight of Mona is 2.5 times that of Hona. The weight of Hona is 1.5 times that of Dhona. The weight of Dhona is 2.5 times that of Rona. Who is the heaviest among Sona, Mona, Hona, Dhona and Rona?

Difficulty: Medium

Correct Answer: Sona

Explanation:


Introduction / Context:
This question presents a chain of comparative statements about the weights of five people: Sona, Mona, Hona, Dhona and Rona. Instead of giving exact weights, it gives ratios that relate one person to another. The task is to reason through these relationships and identify who is the heaviest. This type of problem is common in quantitative aptitude tests and helps develop comfort with ratios and proportional reasoning.


Given Data / Assumptions:

  • The weight of Sona is four times the weight of Mona.
  • The weight of Mona is 2.5 times the weight of Hona.
  • The weight of Hona is 1.5 times the weight of Dhona.
  • The weight of Dhona is 2.5 times the weight of Rona.
  • All weights are positive real numbers.
  • We want to know which person has the greatest weight.


Concept / Approach:
A convenient strategy is to express every person’s weight in terms of a single basic variable, for example the weight of Rona. If the relationships are consistent, we can then see the relative sizes of each person’s weight by comparing the coefficients in front of that variable. The one with the largest coefficient will be the heaviest.


Step-by-Step Solution:
Step 1: Let the weight of Rona be x kilograms. We do not need the exact value of x, only the ratios.Step 2: Dhona’s weight is 2.5 times Rona’s weight, so Dhona weighs 2.5x kilograms.Step 3: Hona’s weight is 1.5 times Dhona’s weight, so Hona weighs 1.5 * 2.5x = 3.75x kilograms.Step 4: Mona’s weight is 2.5 times Hona’s weight, so Mona weighs 2.5 * 3.75x = 9.375x kilograms.Step 5: Sona’s weight is four times Mona’s weight, so Sona weighs 4 * 9.375x = 37.5x kilograms.Step 6: Now compare the coefficients: Rona has x, Dhona has 2.5x, Hona has 3.75x, Mona has 9.375x and Sona has 37.5x.Step 7: Since 37.5x is the largest of these values, Sona is clearly the heaviest.


Verification / Alternative check:
We can also take a simple concrete choice for Rona’s weight, such as x = 2 kilograms, just to check the ordering. Then Dhona weighs 5 kilograms, Hona weighs 7.5 kilograms, Mona weighs 18.75 kilograms and Sona weighs 75 kilograms. The exact numbers do not matter, but the ordering clearly shows that Sona is heavier than Mona, Mona is heavier than Hona, and so on. This numerical example matches the symbolic reasoning and confirms that Sona is the heaviest.


Why Other Options Are Wrong:
Mona is heavy but still lighter than Sona, because Sona is four times Mona. Hona is lighter than Mona because Mona is 2.5 times Hona. Dhona is lighter than Hona since Hona is 1.5 times Dhona. Rona is the lightest because everyone else’s weight is a multiple of Rona’s weight that is greater than 1. Therefore none of these names except Sona can correspond to the heaviest person.


Common Pitfalls:
One common error is to misread the chain and reverse the ratios, for example treating “Mona is 2.5 times Hona” as “Hona is 2.5 times Mona.” Another pitfall is trying to guess the answer without working through all the relationships. Expressing every weight in terms of one base variable keeps the relationships clear and prevents confusion.


Final Answer:
The heaviest person among the five is Sona.

More Questions from Arithmetic Reasoning

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion