Difficulty: Medium
Correct Answer: Statement I alone is sufficient to answer the question but Statement II alone is not.
Explanation:
Introduction / Context:
We are given salary and expenditure ratios for A and B and must determine the ratio of their savings. Data Sufficiency asks which statements pin this down uniquely.
Given Data / Assumptions:
Concept / Approach:
Let Salary(A)=3t and Salary(B)=4t. Savings = Salary − Expenditure. With a saving percentage for B (Statement I), we can find absolute proportions for expenditures and thus A's saving, giving a unique savings ratio.
Step-by-Step Solution:
From I: B's saving = 25% of 4t = t ⇒ B's expenditure = 4t − t = 3t.Expenditure ratio A:B = 4:5 ⇒ Expenditure(A) = (4/5) * 3t = 12t/5.Savings(A) = 3t − 12t/5 = 3t/5.Thus Savings(A):Savings(B) = (3t/5):t = 3:5. Unique ratio obtained ⇒ I alone sufficient.From II alone (B salary ₹2500), without any saving percentage or additional relation, A's saving cannot be deduced ⇒ II alone not sufficient.
Verification / Alternative check:
Actual currency cancels in ratios; therefore numeric salary alone does not help.
Why Other Options Are Wrong:
II alone lacks saving information; combining is unnecessary since I already suffices.
Common Pitfalls:
Using rupee values to force a ratio; remember ratios are scale-free unless a second numerical constraint is provided.
Final Answer:
Statement I alone suffices; savings ratio is 3:5.
Discussion & Comments