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The rate of simple interest on a sum of money is $6$ per cent per annum for the first $3$ years, $8$ per cent per annum for the next $5$ years and $10$ per cent per annum for the period beyond $8$ years. If the simple interest accrued by the sum for a total period of $10$ years is Rs. $1,560,$ what is the sum?

  1. Rs. $1,500$
  2. Rs. $3,000$
  3. Rs. $2,000$
  4. Data Inadequate
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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 $(C).$
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