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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 $(C).$

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 $(C).$