Given,
Rate of interest (R) = 10% p.a.
Time (T) = 3 years
Compound interest - simple interest (CI - SI) = Rs. 3875
To find: Principal (P)
By formula,
Simple interest (SI) = \(\frac{P\times T\times R}{100}\)
= \(\frac{P\times3\times10}{100}\)
= 0.3 P
Again, by formula
Compound interest (CI) = \(P\left\{(1+\frac R{100})^t-1\right\}\)
= \(P\left\{(1+\frac{10}{100})^3-1\right\}\)
= P{(1 + 0.1)3 - 1}
= P{(1.1)3 - 1}
= P(1.331 - 1)
= 0.331P
Now, by the question
CI - SI = Rs. 3875
or, 0.331P - 0.3P = Rs. 3875
or, 0.0031p = Rs. 3875
or, P = \(\frac{Rs.3875}{0.031}\)
or, P = Rs. 125000
Therefore, the required principal (P) is Rs. 125000.