Question

What is the value of ‘a’?
[I.] Ratio of \( a \) and \( b \) is 3 : 5, where \( b \) is positive.
[II.] Ratio of \( 2a \) and \( b \) is \( \dfrac{12}{10} \), where \( a \) is positive.

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

Hint:

Even if both statements provide the same ratio, they may not be sufficient to find a unique value.

Answer 1

The Correct Option is D

From I: \( \dfrac{a}{b} = \dfrac{3}{5} \Rightarrow a = \dfrac{3}{5}b \) From II: \( \dfrac{2a}{b} = \dfrac{12}{10} \Rightarrow \dfrac{a}{b} = \dfrac{6}{10} = \dfrac{3}{5} \) Both statements essentially provide the same ratio \( \dfrac{a}{b} = \dfrac{3}{5} \), but no absolute values. So, \( a \) can be \( 3, 6, 9, \ldots \), and so on — multiple values possible.