A sum of Tk. 1550 was lent partly at 5% and partly at 8% p.a. simple interest. The total interest received after 3 years was Tk. 300. The ratio of the money lent at 5% to that lent at 8% is:

Question: A sum of Tk. 1550 was lent partly at 5% and partly at 8% p.a. simple interest. The total interest received after 3 years was Tk. 300. The ratio of the money lent at 5% to that lent at 8% is:

Solution:
Let
the sum lent at 5% be Tk. x and that lent 8% be Tk. (1550 - x).

ATQ,
(x × 5 × 3)/100 + {(1550 - x) × 8 × 3}/100 = 300
⇒ 15x + 37200 - 24x = 30000
⇒ - 9x = 30000 - 37200
⇒ - 9x = - 7200
⇒ x = 7200/9
∴ x = 800

∴ Required ratio = 800 : 750
= 16 : 15