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MAT Exam 2022 Paper

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Question : 119 of 200

Marks: +1, -0

The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11 : 37. What will be the rate of interest?

36.36%
34.24%
36.26%
38.96%

Solution:

Concept:

Use the difference between compound interest and simple interest for 2 years and 3 years.

Explanation:

Let the rate be

R\%

, so

r = \frac{R}{100}

.

For 2 years:

(\mathrm{CI} - \mathrm{SI})_2 = P r^2

For 3 years:

(\mathrm{CI} - \mathrm{SI})_3 = P r^2 (3 + r)

Given ratio for 2 years to 3 years is

11 : 37

.

Therefore,

\frac{(\mathrm{CI} - \mathrm{SI})_3}{(\mathrm{CI} - \mathrm{SI})_2} = \frac{37}{11}

\frac{P r^2 (3 + r)}{P r^2} = 3 + r = \frac{37}{11}

3 + \frac{R}{100} = \frac{37}{11}

\frac{R}{100} = \frac{37}{11} - 3 = \frac{4}{11}

R = \frac{400}{11} = 36.36\%

Answer:

Rate of interest =

36.36\%

, i.e. Option A.

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