Question

A total amount of interest earned on a certain sum for 2 years is ₹684 .And for 3 years is ₹1084.Find the rate of interest.​

Answer 1

16.66%

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Answer 2

Given :- A total amount of interest earned on a certain sum for 2 years is ₹684 .And for 3 years is ₹1084.Find the rate of interest.

Solution :-

Let us assume that, rate of interest is R% per annum and Principal is Rs.P .

so,

→ CI for 2 years = P[{1 + (R/100)}² - 1] = 684

and,

→ CI for 3 years = P[{1 + (R/100)}³ - 1] = 1084

Let us assume that, {1 + (R/100)} = x .

then,

→ (2 year CI / 3 year CI) = (x² - 1) / (x³ - 1) = 684/1084

→ (x - 1)(x + 1)/(x - 1)(x² + x + 1) = 171/271

→ (x + 1)/(x² + x + 1) = 171/271

→ 271x + 271 = 171x² + 171x + 171

→ 171x² - 100x - 100 = 0

→ 171x² - 190x + 90x - 100 = 0

→ 19x(9x - 10) + 10(9x - 10) = 0

→ (19x + 10)(9x - 10) = 0

→ x = (-10/19) or (10/9)

taking x = (-10/19) , we get,

→ 1 + (R/100) = (-10/19)

→ (R/100) = (-10/19) - 1

→ (R/100) = (-29/19)

→ R = (-2900/19) = Negative integer not possible .

and, taking x = (10/9) , we get,

→ 1 + (R/100) = (10/9)

→ (R/100) = (10/9) - 1

→ R/100 = (1/9)

→ R = (100/9) % (Ans.)

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