Difficulty: Medium
Correct Answer: Both I and II are necessary to answer
Explanation:
Introduction:
This is a data sufficiency question for simple interest where the interest amount is known but principal is not. Simple interest depends on principal P, rate r, and time t via SI = (P * r * t)/100. To determine P uniquely, we must know both r and t (or otherwise have enough information to infer them). The task is to check whether statement I or II alone is sufficient, or whether both are required.
Given Data / Assumptions:
Concept / Approach:
Evaluate sufficiency of each statement. If only r is known, then SI = (P * r * t)/100 still has two unknowns (P and t). If only t is known, it has two unknowns (P and r). Only when both r and t are known can we solve uniquely for P using P = (SI * 100) / (r * t).
Step-by-Step Solution:
Using SI = (P * r * t)/100
Check Statement I alone: r = 10%, but t is unknown, so P cannot be uniquely found.
Check Statement II alone: t = 10 years, but r is unknown, so P cannot be uniquely found.
Using I and II together: r = 10 and t = 10
P = (SI * 100) / (r * t) = (50 * 100) / (10 * 10) = 5000 / 100 = 50
Verification / Alternative check:
If P = ₹50 at 10% for 10 years, SI = (50 * 10 * 10)/100 = 50, matching the given interest. This confirms that with both statements, the principal is uniquely determined.
Why Other Options Are Wrong:
Options claiming I alone or II alone is sufficient are incorrect because each leaves two unknowns. “Either I or II alone” is also incorrect for the same reason. “Even together not sufficient” is false because together they give an exact P.
Common Pitfalls:
Assuming a default time or rate, confusing simple interest with compound interest, or thinking that knowing SI and one of r or t automatically fixes P (it does not).
Final Answer:
Both I and II are necessary to determine the principal.
Discussion & Comments