Question

What is the simple interest earned yearly on a deposit in a bank? I) The amount deposited is rupees \(10,000\).
II) The rate of interest is \(8\%\) per annum.

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question
• C. Both the statements I and II are sufficient to answer the question but neither statement alone is not sufficient
• D. Both the statements I and II together are not sufficient to answer the question and additional data is required

Hint:

For simple interest, principal, rate and time are required. If any one of them is missing, the interest cannot be calculated.

Answer 1

The Correct Option is C

Concept:
Simple interest for one year is calculated by the formula \[ SI=\frac{P\times R\times T}{100} \] where \[ P=\text{Principal amount} \] \[ R=\text{Rate of interest} \] \[ T=\text{Time in years} \] Since the question asks for yearly simple interest, \[ T=1 \]

Step 1: Check Statement I. Statement I says: \[ P=10000 \] But the rate of interest is not given. So simple interest cannot be found using Statement I alone. Therefore, Statement I alone is not sufficient.

Step 2: Check Statement II. Statement II says: \[ R=8\% \] But the principal amount is not given. So simple interest cannot be found using Statement II alone. Therefore, Statement II alone is not sufficient.

Step 3: Combine both statements. Using both statements, \[ P=10000,\qquad R=8,\qquad T=1 \] So, \[ SI=\frac{10000\times 8\times 1}{100} \] \[ SI=800 \] Thus, both statements together are sufficient.

Step 4: Final answer. \[ \boxed{\text{Both statements together are sufficient, but neither alone is sufficient}} \]