Explanation:

- Raja borrowed Rs15,000 at a simple interest rate of 13% per annum.

- The simple interest formula is $SI=P\times R\times T/100$.

- For two years, simple interest: $SI=15000\times 13\times 2/100=Rs3,900$.

- The total amount Raja needs to pay back is Rs15,000 + Rs3,900 = Rs18,900.

- He lent Rs15,000 at a compound interest rate of 15% per annum.

- The compound interest formula is $A=P\times (1+R/100{)}^T$.

- For two years, compound interest: $A=15000\times (1+15/100{)}^2=Rs19,837.50$.

- Raja's gain is the difference: Rs19,837.50 - Rs18,900 = Rs937.50.

- Option 3: Rs937.50 is the correct option.

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