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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