Question

Salary of A and B is in ratio 3:4 and expenditure is in ratio 4:5. What is the ratio of their saving?
(I) B's saving is 25% of his salary.
(II) B's salary is Rs 2500.

• A. Answer (1) if data in Statement I alone is sufficient to answer the question but the data in Statement II alone is not sufficient to answer the question.
• B. Answer (2) if data in Statement II alone is sufficient to answer the question but the data in Statement I alone is not sufficient to answer the question.
• C. Answer (3) if data in Statement I and II together are necessary to answer the question.
• D. Answer (4) if data in Statement I and II together are not sufficient to answer the question.

Hint:

Express salaries as 3k, 4k and expenditures as 4m, 5m; check which statement pins down the ratio 3k-4m to 4k-5m on its own.

Answer 1

The Correct Option is A

Step 1: Set up variables for salary and expenditure.
Let A's salary be 3k and B's salary be 4k for some positive number k, matching the given salary ratio 3:4. Let A's expenditure be 4m and B's expenditure be 5m for some positive number m, matching the given expenditure ratio 4:5. Then A's saving is 3k - 4m and B's saving is 4k - 5m; the question asks for the ratio (3k-4m):(4k-5m).
Step 2: Test Statement I alone.
Statement I says B's saving is 25% of B's salary, i.e. 4k - 5m = 0.25 x 4k = k. Solving, 5m = 4k - k = 3k, so m = 3k/5. Substitute this back into A's saving: 3k - 4m = 3k - 4(3k/5) = 3k - 12k/5 = 3k/5. B's saving is k. So the ratio of savings is 3k/5 : k = 3:5. The value k cancels out entirely, so this ratio is fixed no matter what k actually is. Statement I alone is sufficient.
Step 3: Test Statement II alone.
Statement II says B's salary is Rs. 2500, i.e. 4k = 2500, so k = 625. This pins down k, but m, which governs the expenditure amounts, remains completely unknown, since expenditure was only given as a ratio 4:5, not tied to an actual value. Without knowing m, neither A's saving, nor B's saving, nor their ratio can be found. Statement II alone is not sufficient.
Step 4: Conclusion.
Statement I alone is sufficient to find the saving ratio, but Statement II alone is not. This matches option (1).