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Let $A = \{2, 3, 4, 5......, 30\}$ and “ $≃$ ” be an equivalence relation on $A \times A$ defined by $(a, b) ≃ (c, d)$ ,
if and only if $a d = b c$ .Then the number of ordered pairs which satisfy this equivalence relation with ordered pair $(4, 3)$ is equal to:

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answer is C.

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Detailed Solution

$\begin{array}{l} (a, b) R (c, d) \Rightarrow a d = b c \\ ∴ (a, b) R (4, 3) \Rightarrow 3 a = 4 b \\ ∴ (a, b) = (4, 3), (8, 6), (12, 9), (16, 12), (20, 15) (24, 18), (28, 21) \end{array}$

Total ordered pairs is 7

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