#### The simple interest on a certain sum for 3 years is ₹ 225 and the compound interest on the same sum at the same rate for 2 years is ₹ 153. Find the rate of interest and the principal.

**Solution:**

It is given that

SI for 3 years = ₹ 225

SI for 2 years = (225 × 2)/ 3 = ₹ 150

CI for 2 years = ₹ 153

So the difference = 153 – 150 = ₹ 3

Here ₹ 3 is interest on one year i.e. ₹ 75 for one year

We know that

Rate = (SI × 100)/ (P × t)

Substituting the values

= (3 × 100)/ (75 × 1)

= 4%

SI for 3 years = ₹ 225

Rate = 4% p.a.

So principal = (SI × 100)/ (R × t)

Substituting the values

= (225 × 100)/ (4 × 3)

= ₹ 1875

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