Total money with Naresh and Ajay is 28 percent of that with Usman. How much money does Ajay have? Consider the following statements: I. Usman has a total of Rs 75000. II. The ratio of the money of Naresh to the money of Ajay is 1 : 3. Using the data above, determine which statement or statements are sufficient to find the exact amount of money with Ajay.

Introduction / Context:
This question is a classic example of data sufficiency in percentage and ratio based word problems. The total money held by Naresh and Ajay is given as a fixed percentage of Usman amount, and two statements provide additional numerical details. The task is to decide which combination of statements allows us to compute Ajay exact amount, not simply to perform that calculation.

Given Data / Assumptions:

• The combined money of Naresh and Ajay is 28 percent of the total money of Usman.
• Statement I says that Usman has Rs 75000.
• Statement II says that the ratio of the amount of Naresh to the amount of Ajay is 1 : 3.
• All amounts are assumed to be positive real numbers expressed in rupees.

Concept / Approach:
We translate the information into algebraic equations. Let U, N, and A denote the amounts of Usman, Naresh, and Ajay. The percentage relation gives N + A as a fixed percentage of U. The ratio relation gives N and A in a fixed ratio. We then check which statements give enough equations to determine A uniquely. If a statement alone leaves free variables, it is not sufficient; if both together close the system, they are necessary.

Step-by-Step Solution:
Step 1: From the initial condition we have N + A = 28 percent of U, so N + A = 0.28 * U. Step 2: From statement I, U = 75000. Substituting into the earlier equation gives N + A = 0.28 * 75000 = 21000. Therefore the sum of the amounts of Naresh and Ajay is 21000, but the individual portions N and A are still unknown. Step 3: Notice that with statement I alone, there are infinitely many pairs (N, A) such that N + A = 21000, so the amount of Ajay cannot be fixed. Statement I alone is not sufficient. Step 4: From statement II, N : A = 1 : 3. That means N = k and A = 3k for some positive constant k. However, without knowing N + A or some other relation connecting their sum to a number, k remains free. Statement II alone is therefore not sufficient. Step 5: Combine statements I and II. From earlier, N + A = 21000 and N : A = 1 : 3. Substitute N = k and A = 3k. We get k + 3k = 21000, so 4k = 21000, and k = 5250. Hence N = 5250 and A = 15750. Now Ajay amount is uniquely determined. Step 6: Since neither statement alone is sufficient, but their combination yields a unique value for Ajay, we classify the sufficiency as requiring both statements together.

Verification / Alternative check:
A quick alternative check is to count unknowns and equations. Without using any statements, we have three unknowns U, N, and A and one relation N + A = 0.28 * U. Statement I adds a second equation by fixing U, and statement II adds a third equation by fixing the ratio of N to A. With all three relations, the system becomes determined and allows exact computation of N and A. Removing either statement removes one equation and leaves infinitely many solutions, which confirms that both statements are necessary.

Why Other Options Are Wrong:
Option A is wrong because statement I alone stops at N + A = 21000, without a way to split that sum between Naresh and Ajay. Option B is wrong because statement II alone only fixes the ratio and never gives a total. Option C, suggesting that either statement alone suffices, is clearly incorrect. Option E, which claims that even both statements together are not sufficient, is also wrong because the combination gives a fully determined system and leads to a unique value for Ajay amount. Only option D correctly identifies that both statements together are necessary to get the exact figure.

Common Pitfalls:
A common mistake is to assume that knowing the percentage relation and Usman amount automatically gives Ajay amount, without noticing that the combined amount includes Naresh as well. Another error is to misread the ratio 1 : 3 as giving absolute numbers instead of proportional values. In data sufficiency questions, it is important to separate information about totals from information about ratios and ensure both are present before concluding that a single share can be computed.

Final Answer:
The data in both statements I and II together are necessary to answer the question, so the correct option is D.