A sum of Rs 1085 is lent out in two parts on Simple interest in such a way that the interest on one part at 9% for 3 years is equal to that…

Let two parts of the sum be Rs. a and Rs. b respectively.

Given, a + b = 1085

Let P = principal, R = rate of interest and N = time period

Simple interest = PNR/100

According to the question,

⇒ (a × 9 × 3)/100 = (b × 18 × 2)/100

⇒ 27a = 36b

⇒ 3a = 4b

⇒ a = 4b/3

Solving equations,

⇒ 4b/3 + b = 1085

⇒ 7b = 1085 × 3

⇒ b = 465

⇒ a = 1085 – 465 = 620

∴ Two sums are Rs. 620 and Rs. 465.