Question

pls help me with the 23rd sum

Answer 1

Let the sum = Rs x and rate of interest = r%
Simple interest for three years = P*T*R/100 = x*3*r/100 = Rs 3xr/100
Amount for three years = sum + interest for 3 years
Rs 4745 = Rs x + Rs 3xr/100
4745 = (100x+3xr)/100
474500 = 100x + 3xr
474500 - 100x = 3xr
r = (474500 - 100x)/3x %

Now interest for 5 years = P*T*R/100 = x*5*r/100 = Rs 5xr/100
Amount for 5 years = sum + interest for 5 years
Rs 5475 = Rs x + Rs 5xr/100
5475 = (100x+5xr)/100
547500 = 100x + 5xr
5xr = 547500 - 100x
r = (547500-100x)/5x %

Therefore
(474500 - 100x)/3x = (547500-100x)/5x
(474500-100x)/3 = (547500-100x)/5
(474500-100x)5 = (547500-100x)3
2372500 - 500x = 1642500 - 300x
200x = 730000
x = 730000/200 = Rs 3650
sum = Rs 3650

r = [474500 - 100(3650)]/3*3650
r = (474500 - 365000)/10950
r = 109500/10950 = 10%
Rate of interest = 10%