If Simple Interest is 12.5% more than the principal and number of years(n) , rate(r) are numerically in the ratio 2 : 1 , then find the values of n , r.
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A.
n =20, r=10%
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B.
n = 14; r = 7%
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C.
n =12, r =6%
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D.
n=15, r=7 1/2 %
Correct Answer:
D. n=15, r=7 1/2 %
Explanation:
To find the values of the number of years (n) and the rate of interest (r), we use the simple interest formula: SI = (P * r * n) / 100. Given information:1. Simple Interest (SI) is 12.5% more than the principal (P). This can be expressed as SI = P + 0.125P = 1.125P. 2. The ratio of n to r is 2 : 1, which means n = 2x and r = x.Step-by-step calculation: - Substitute the known values into the simple interest formula: 1.125P = (P \* x \* 2x) / 100. - Cancel out P from both sides: 1.125 = 2x^2 / 100. - Multiply both sides by 100: 112.5 = 2x^2. - Divide by 2: 56.25 = x^2. - Take the square root of both sides: x = 7.5.Since r = x and n = 2x: - r = 7.5% (or 7 1/2 %) - n = 2 \* 7.5 = 15 yearsTherefore, the correct values are n = 15 and r = 7 1/2 %.
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