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

Work with percentages instead of raw variables to double-check the result from a different angle.

Let A's salary $=3x$ and B's salary $=4x$. Let A's expenditure $=4y$ and B's expenditure $=5y$.

Statement I fixes B's saving as a fraction of B's salary: saving of B $= 4x - 5y = 0.25(4x) = x$. This single equation relates $x$ and $y$ directly: $5y = 3x$, so $y = 0.6x$.

Now find A's saving using this relation:

\[\text{Saving of A} = 3x - 4y = 3x - 4(0.6x) = 3x - 2.4x = 0.6x\]

The savings ratio is then:

\[\text{Saving of A} : \text{Saving of B} = 0.6x : x = 3 : 5\]

This ratio has no leftover unknown in it, since the variable $x$ cancels completely, so Statement I alone answers the question on its own, regardless of the actual salary figures.

Statement II, by contrast, only tells us $4x = 2500$, fixing $x = 625$ in rupees. That pins down both salaries exactly, but expenditure was defined only through the separate variable $y$, and nothing in Statement II constrains $y$. Infinitely many values of $y$ remain possible, each giving a different savings ratio, so Statement II alone cannot answer the question.

Therefore Statement I alone is sufficient while Statement II alone is not, confirming option (1): the ratio of savings is \(\boxed{3:5}\), obtainable from Statement I alone.