Question

Radha and Rani appeared in an examination. What was the total number of questions?
[I.] Radha and Rani together solved 20% of the paper.
[II.] Radha alone solved \( \dfrac{3}{5} \) of the paper solved by Rani.

• A. if the question can be answered with the help of any one statement alone but not by the other statement.
  % Optio
• B. if the question can be answered with the help of either of the statements taken individually.
  % Optio
• C. if the question can be answered with the help of both statements together.
  % Optio
• D. if the question cannot be answered even with the help of both statements together.

Hint:

When total is not given and only proportions are, check if absolute values can be determined.

Answer 1

The Correct Option is D

Let total number of questions = \( x \). Let Radha solved \( r \), Rani solved \( R \). Then: From Statement I: \( r + R = 0.2x \) — one equation with two variables. From Statement II: \( r = \dfrac{3}{5} R \) — another relation. Using both: \[ \frac{3}{5}R + R = 0.2x \Rightarrow \frac{8}{5}R = 0.2x \Rightarrow R = \frac{1}{8}x \Rightarrow r = \frac{3}{5} \cdot \frac{1}{8}x = \frac{3x}{40} \] Still we get: \[ r = \frac{3x}{40},\quad R = \frac{x}{8} \Rightarrow \text{But no unique value of } x. \] So we only get ratios, not actual value of \( x \). Not sufficient.