Arun's weight is 140% of Akhil's weight. Shreyon's weight is twice Akhil's weight, and Nani's weight is 90% of Shreyon's weight. Nani's weight is what percentage of Arun's weight?

Introduction / Context:
This question deals with chained percentage relationships between the weights of four people. Such problems are common in percentage comparison and ratio topics, where each quantity is defined in terms of another, and we need to express one final quantity as a percentage of another. The key is to choose a base variable, express all weights in terms of that, and then compare the two required values.

Given Data / Assumptions:

Let Akhil's weight be A.
Arun's weight is 140% of Akhil's weight, so Arun = 1.4A.
Shreyon's weight is twice Akhil's weight, so Shreyon = 2A.
Nani's weight is 90% of Shreyon's weight, so Nani = 0.9 * 2A.
We need Nani's weight as a percentage of Arun's weight.

Concept / Approach:
All weights are expressed as multiples of Akhil's weight A. Once these expressions are set up, we only need the ratio of Nani to Arun, because the base A cancels out. The formula we use is:
percentage of Arun represented by Nani = (Nani / Arun) * 100 This method avoids the need for actual numerical weights and works with pure ratios and percentages.

Step-by-Step Solution:
Step 1: Express all weights in terms of A. Arun = 1.4A. Shreyon = 2A. Nani = 90% of Shreyon = 0.90 * 2A = 1.8A. Step 2: Form the ratio Nani / Arun. Nani / Arun = (1.8A) / (1.4A). Step 3: Cancel A from numerator and denominator. Nani / Arun = 1.8 / 1.4. Step 4: Simplify 1.8 / 1.4. 1.8 / 1.4 = 18 / 14 = 9 / 7. Step 5: Convert this ratio to a percentage. (9 / 7) * 100 ≈ 128.5714%. Step 6: Rounded to one decimal place this is about 128.6%. Therefore, Nani's weight is approximately 128.6% of Arun's weight.

Verification / Alternative check:
For a quick check, we can assign a convenient value to A, say Akhil weighs 50 kg. Then Arun weighs 1.4 * 50 = 70 kg. Shreyon weighs 2 * 50 = 100 kg. Nani weighs 0.9 * 100 = 90 kg. Now compute Nani as a percentage of Arun: (90 / 70) * 100 = (9 / 7) * 100 ≈ 128.57%. This again confirms that Nani is about 128.6% of Arun in weight.

Why Other Options Are Wrong:
120% and 125% are both less than the accurate value of about 128.6%, so they underestimate Nani's weight relative to Arun.
130% and 135% both overestimate the ratio, with 135% being significantly higher than the exact value of about 128.6%.
Only 128.6% matches the computed ratio closely.

Common Pitfalls:
Many learners accidentally compare Nani to Akhil or Shreyon instead of to Arun, leading to different percentages. Another typical error is to add or subtract the percentages linearly instead of expressing them as multipliers. Confusing which person is the base for each percentage (for example, mixing up 140% of Akhil and 90% of Shreyon) can also lead to mistakes. Always express each quantity cleanly in terms of a single base variable to avoid confusion.

Final Answer:
Nani's weight is approximately 128.6% of Arun's weight.