Question

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

• A. 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. 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. Data in both statements I and II together are necessary to answer the question.
• D. Data in both statements I and II together are not sufficient to answer the question.

Answer 1

The Correct Option is A

The problem requires determining the ratio of savings for two individuals, A and B, given the ratios of their salaries and expenditures. We are provided with two statements and must assess their sufficiency. 

1. Let's define the variables:
Let the salary of A be \(3x\) and the salary of B be \(4x\).
Their expenditures are in the ratio 4:5, so let A's expenditure be \(4y\) and B's expenditure be \(5y\).

2. We need to find the savings ratio for A and B, defined as savings = salary - expenditure.

3. Statement I: B's saving is 25% of his salary.

B's saving = \(0.25 \times 4x = 1x\).
B's expenditure = salary - saving = \(4x - 1x = 3x\).
Since B's expenditure relates to \(5y\), we have \(5y = 3x\) and can solve for \(y\) in terms of \(x\): \(y = \frac{3x}{5}\).

A's expenditure = \(4y = 4 \times \frac{3x}{5} = \frac{12x}{5}\).
A's saving = \(3x - \frac{12x}{5} = \frac{15x}{5} - \frac{12x}{5} = \frac{3x}{5}\).
The ratio of A's saving to B's saving is \(\frac{\frac{3x}{5}}{x} = \frac{3}{5}\).
Therefore, statement I is sufficient.

4. Statement II: B's salary is Rs. 2500.

If B's salary is Rs. 2500, we know \(4x = 2500\) or \(x = 625\), but without information on the percentage saved or additional details about A's salary, we can't determine savings ratio. Statement II alone is not sufficient.

5. Conclusion: 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.