What is the total monthly salary of Vasu? Consider the following statements: I. The basic salary of Vasu is Rs 100 more than the basic salary of Rajan, who also works in the same company. II. Other allowances drawn by Rajan, in addition to his basic salary, are Rs 2000 per month, which is Rs 50 less than the allowances drawn by Vasu. III. The basic salary of Rajan is Rs 1550 per month.

Introduction / Context:
This data sufficiency question concerns salaries and allowances of two employees, Vasu and Rajan. The goal is to decide which combination of three statements allows us to compute Vasu total monthly salary, including basic salary and allowances. The question tests how well the learner can translate verbal descriptions of salary structure into equations and see which data points are essential.

Given Data / Assumptions:

• Vasu and Rajan work in the same company.
• Statement I: The basic salary of Vasu is Rs 100 more than the basic salary of Rajan.
• Statement II: Rajan draws allowances of Rs 2000 per month, and these allowances are Rs 50 less than the allowances drawn by Vasu.
• Statement III: The basic salary of Rajan is Rs 1550 per month.
• Total salary is taken as basic salary plus allowances for each employee.

Concept / Approach:
Let RB and VB denote the basic salaries of Rajan and Vasu, and RA and VA denote their monthly allowances. Vasu total salary is VB + VA. We must examine which statements give enough numeric information to evaluate VB and VA. If any combination leaves one of these variables undetermined, that combination is not sufficient. We are not concerned with computing the final number for the exam, but doing so acts as a useful check.

Step-by-Step Solution:
Step 1: Translate statement I into an equation. If RB is the basic salary of Rajan, then VB = RB + 100. Step 2: Translate statement II. Rajan has allowances RA = 2000, and these allowances are Rs 50 less than Vasu allowances. So VA = RA + 50 = 2000 + 50 = 2050. Step 3: Translate statement III. It directly gives RB = 1550. Step 4: Check statement II alone. Knowing only that Vasu allowances are Rs 2050 does not provide any information about VB. Therefore, statement II alone is not sufficient to compute the total salary of Vasu. Step 5: Check statements II and III together. From III, RB = 1550. From II, VA = 2050. However, Vasu basic salary VB still depends on statement I, since we only know the relation between VB and RB from I. Without I, VB remains unknown, so the combination of II and III is not sufficient. Step 6: Check statements I and II together. With I, we know VB = RB + 100, and with II, VA = 2050. Without having a numeric value for RB, VB remains unknown, and therefore VB + VA cannot be computed. So I and II together are also not sufficient. Step 7: Combine all three statements. Using III, RB = 1550. Substituting into I gives VB = 1550 + 100 = 1650. From II we already know VA = 2050. Therefore Vasu total monthly salary is VB + VA = 1650 + 2050 = 3700 rupees. With all three statements, the total is uniquely determined.

Verification / Alternative check:
To verify, we can reason from the perspective of unknowns and equations. The key unknowns affecting Vasu salary are VB and VA. Statement I relates VB to RB, so VB depends on knowing RB. Statement II gives VA numerically but still requires VB. Statement III gives RB numerically. Only when all three statements are used do we have numeric values for both VB and VA. Any subset of statements leaves VB or VA unspecified, which means Vasu total salary is not fixed. This confirms that all three statements are required.

Why Other Options Are Wrong:
Option A is incorrect because statement II alone does not say anything about Vasu basic salary. Option B, which gives sufficiency to II and III, fails since VB still cannot be calculated without the link provided by statement I. Option C, involving I and II, is also not enough because RB remains unknown without statement III. Only option D correctly recognises that statements I, II, and III together are required to answer the question.

Common Pitfalls:
One common mistake is to misread statement II and assume that the allowances figure includes Vasu basic salary or that Vasu salary itself is Rs 50 more than some number. Another typical error is to think that relative information such as Rs 100 more is enough without a base figure. In salary questions, relative differences must be anchored by at least one concrete value before totals can be found.

Final Answer:
The total monthly salary of Vasu can be determined only when statements I, II, and III are all used together, so the correct option is D.