Sneha’s weight is 140% of Veena’s weight. Rina’s weight is 90% of Sana’s weight, and Sana weighs twice as much as Veena. If Sneha’s weight is x% of Rina’s weight, what is the value of x?

Introduction / Context:
This problem links four people's weights with several percentage relationships. Sneha's weight is described relative to Veena's, Rina's relative to Sana's, and Sana's relative to Veena's. From these, we must find the percentage that Sneha's weight represents of Rina's weight. Such chained percentage ratio questions are typical in quantitative aptitude tests and require clear variable assignment and algebraic manipulation.

Given Data / Assumptions:

Let Veena's weight be V.

Sneha's weight is 140% of Veena's weight.

Sana's weight is twice Veena's weight.

Rina's weight is 90% of Sana's weight.

We must find x such that Sneha's weight is x% of Rina's weight.

Concept / Approach:
We express all weights in terms of the common base V (Veena's weight). Percentages are converted to multiplication factors. Then we write Sneha's and Rina's weights in these terms, form the ratio Sneha / Rina, and convert this ratio into a percentage. This method avoids dealing with specific numbers and highlights the proportional structure of the problem.

Step-by-Step Solution:
Let Veena's weight be V.Sneha's weight is 140% of V, so Sneha = 1.40V.Sana's weight is twice Veena's weight, so Sana = 2V.Rina's weight is 90% of Sana's weight, so Rina = 0.90 * Sana = 0.90 * 2V = 1.80V.We need x such that Sneha = (x / 100) * Rina.That is, 1.40V = (x / 100) * 1.80V.Divide both sides by V: 1.40 = (x / 100) * 1.80.So x / 100 = 1.40 / 1.80.Simplify 1.40 / 1.80 = 14 / 18 = 7 / 9.Thus x / 100 = 7 / 9, so x = (7 / 9) * 100 = 700 / 9.

Verification / Alternative check:
We can choose a convenient value for V to check. Let V = 9 kg. Then Sneha's weight = 1.40 * 9 = 12.6 kg. Sana's weight = 2 * 9 = 18 kg. Rina's weight = 0.90 * 18 = 16.2 kg. Now find what percent Sneha is of Rina: (12.6 / 16.2) * 100. Compute 12.6 / 16.2 = 7 / 9. Hence the percentage is (7 / 9) * 100 = 700 / 9. This confirms the algebraic result.

Why Other Options Are Wrong:

596/9, 605/9, 645/9 and 650/9 are all different from 700/9 and arise from incorrect algebra, wrong percentage conversions, or misinterpreting which weight is being compared to which.

Only 700/9 exactly equals (Sneha / Rina) * 100 when the correct relationships are applied.

Common Pitfalls:
Students sometimes mix up the direction of percentage relationships, for example thinking Sana is 90% of Rina instead of Rina being 90% of Sana. Others may fail to use a common base like Veena's weight and instead attempt to guess numbers, which can lead to arithmetic confusion. Another mistake is to divide the wrong way when forming the ratio Sneha / Rina, which inverts the percentage. Carefully expressing all quantities in terms of V and proceeding step by step prevents these errors.

Final Answer:
The value of x, the percentage that Sneha's weight is of Rina's weight, is 700/9 percent.