Explanation:

- To find the original rate of interest, use the formula for simple interest: $SI=\frac{P\cdot R\cdot T}{100}$.

- Given: Principal $P=15,000$, Time $T=5$ years, Simple Interest $SI=9,750$.

- Solve for $R$: $9,750=\frac{15,000\cdot R\cdot 5}{100}$.

- Results in $R=13\mathrm{\%}$.

- If the rate is 3% lesser, the new rate $R^{\prime }$ is 10%.

- Calculate the new interest:

- New $S{I}^{\prime }=\frac{15,000\cdot 10\cdot 5}{100}=7,500$.

- Options:

- Option 1: Rs9,750 - This is the original interest, not the new one.

- Option 2: Rs5,850 - Incorrect calculation.

- Option 3: Rs3,250 - Incorrect calculation.

- Option 4: Rs7,500 - Correct new interest amount.

Option 4: Rs7,500

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