A man lends Tk. 5000 in three parts at different rates of simple interest per annum. If he gets 4% on TK. 1500 and 5% on TK. 2500, what percent must he get for the remainder, if the average rate of simple interest per annum is 5.5%?

Question: A man lends Tk. 5000 in three parts at different rates of simple interest per annum. If he gets 4% on TK. 1500 and 5% on TK. 2500, what percent must he get for the remainder, if the average rate of simple interest per annum is 5.5%?

Solution:
Total Principal, P = 5000 TK.
Average Interest Rate = 5.5%
Total Interest required = (5000 × 5.5)/100 = 275 TK.

Interest from 1st part (1500 at 4%) = (1500 × 4)/100 = 60 TK.
Interest from 2nd part (2500 at 5%) = (2500 × 5)/100 = 125 TK.

Total interest from these two parts = 60 + 125 = 185 TK.
Remaining Interest needed = 275 - 185 = 90 TK.

Remaining Principal = 5000 - (1500 + 2500) = 1000 TK.

Let the required rate for the remainder be r%.
Using SI = Pnr/100 (where n = 1 year):
⇒ 90 = (1000 × 1 × r)/100
⇒ 90 = 10r
⇒ r = 90/10
⇒ r = 9

So, he must get 9% interest for the remainder.