We know that $SI = \dfrac{P \times R \times T}{100}$
Now, $\dfrac{P\cdot 6\cdot 3}{100} + \dfrac{P\cdot 8\cdot 5}{100} + \dfrac{P\cdot 10\cdot 2}{100} = Rs.\;1,560$
$\implies \dfrac{18P + 40P + 20P}{100} = Rs.\;1,560$
$\implies P = Rs.\;2,000.$
So, the correct answer is $(C).$