Test Index

MAT Exam 2021 Paper

Question : 95 of 200

Marks: +1, -0

Solution:

Concept:

Compare compound interest (CI) with simple interest (SI) for 2 and 3 years to first find the rate, then the principal.

Explanation:

Let the sum be

P

and the annual rate be

R\%

. Put

r = \frac{R}{100}

For the first 2 years,

CI - SI = 20

\left[P(1+r)^2 - P\right] - 2Pr = 20

Expanding and simplifying:

P r^2 = 20

For the first 3 years,

CI - SI = 61

\left[P(1+r)^3 - P\right] - 3Pr = 61

P r^3 + 3P r^2 = 61

Using

P r^2 = 20

, we get:

20r + 60 = 61

r = \frac{1}{20} = 0.05

So the rate is

R = 5\%

Now substitute into

P r^2 = 20

P(0.05)^2 = 20

P = \frac{20}{0.0025} = 8000

Answer:

The required sum is ₹8000, i.e. option C.

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