Given that $,A + B = ₹1210$
If $\dfrac{4}{15}$ of A′s amount is equal to $\dfrac{2}{5}$ of B′s amount.
$\implies \dfrac{4}{15}A = \dfrac{2}{5}B$
$\implies \dfrac{2}{3}A = B$
$\implies A = \dfrac{3}{2}B$
Now, $A+B = ₹1210$
$\implies \dfrac{3}{2}B + B = ₹1210$
$\implies \dfrac{3B + 2B}{2} =₹1210$
$\implies 5B = ₹2420$
$\implies B = ₹484.$
So, the correct answer is $(C).$