Question

if the ratio of principal and amount after 13 years at simple interest becomes 9:17 and after 27.5 years more ratios. becomes 15:43 find the rate of interest

Answer 1

The rate of interest is 3.2%

Step-by-step explanation:

From question, after 13 years at simple interest becomes 9 : 17 which is:

P = 9x and A = 17x

⇒ P + (Simple interest after 3 years) = Rs. 17x → (equation 1)

From question, after 27.5 years more ratio becomes 15 : 43 which is:

P : [P + (Simple interest after 30.5 years)] = 15 : 43 = 1 : 43/15 = (9x × 1) : (9x × 43/15) = 9x : 129x/5

⇒ [P + (Simple interest after 30.5 years) = 129x/5 → (equation 2)

Now, equation (2) - equation (1), we get,

The simple interest after 27.5 years = 129x/5 - 17x = (129 - 85)x/5 = 44x/5

Now, the rate of interest is given as:

r = (44x/5 × 100)/(9x × 30.5) = (44x × 20)/(9x × 30.5) = 880x/274.5x

∴ r = 3.2%