Question

Daniel deposits ₹10000 in a fixed deposit earning \( p\% \) annual interest, compounded quarterly. What is the value of \( p \)? Statement (I): He would have earned ₹18 less for the deposit period had he been paid simple interest.
Statement (II): He withdraws all the money six months after depositing it.

• A. Statement (I) alone is sufficient.
• B. Statement (II) alone is sufficient.
• C. Both statements (I) and (II) are sufficient.
• D. Neither statement is sufficient.

Hint:

A relationship involving compound interest usually requires both the rate and the time period. If either is missing, the information is often insufficient.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem requires finding the overall percentage change in a rectangle's area after its length is increased by a certain percentage and its breadth is decreased by the same percentage.


Step 2: Key Formula or Approach:
Rectangle Area = \(\text{Length} \times \text{Breadth}\).
For consecutive percentage modifications \(x\) and \(y\), the net percentage change is found via the formula:
\[ \text{Net Change \%} = \left( x + y + \frac{x \times y}{100} \right) \% \]

Step 3: Detailed Explanation:
Assume the initial length is \(L\) and the initial breadth is \(B\).
Initial Area \(A = L \times B\).
A 10% length increase makes the new length \(1.1L\).
A 10% breadth decrease makes the new breadth \(0.9B\).
New Area \(A' = 1.1L \times 0.9B = 0.99LB\).
This shows the new area is 99% of the original, signifying a 1% reduction (\(100\% - 99\%\)).
Alternative method using the formula:
Assign \(x = +10\) (for increase) and \(y = -10\) (for decrease).
\[ \text{Net Change \%} = 10 - 10 + \frac{10 \times (-10)}{100} = 0 - \frac{100}{100} = -1\% \] The negative result confirms a 1% decrease.


Step 4: Final Answer:
The correct choice is (B).