$(SI = \frac{{P \times R \times T}}{{100}})$

Where, SI – Simple Interest

P – Principal

R – rate

T – time

Given, sum is invested at a certain annual rate of simple interest for 4 years. Rs. 355 is the increase in interest if the rate of interest is increased by 5% of initial rate.

$(SI\; = \frac{{\;P\; \times \;R\; \times \;4}}{{100}}\; = \frac{{PR}}{{25}})$

Increased rate = R + 5% of R = 1.05R

$(SI\; = \frac{{P\; \times \;1.05R\; \times \;4}}{{100}} = \frac{{1.05PR}}{{25}})$

Given, difference between the two interests is Rs. 355

$(\therefore \frac{{1.05PR}}{{25}} - \frac{{PR}}{{25}} = 355)$

R = 10%

⇒0.05 × P × 10 = 355 × 25