Question

A sum of money becomes 9 times in 20 years. Find the rate of interest

Answer 1

Step-by-step explanation:

Let the principal =Rs.x, Amount =Rs.3x, Time =20 years

∴S.I.=Rs.3x−Rs.x=Rs.2x

Rate =( x×202x×100 )%p.a.=10%p.a.

Now, Principal =Rs.x, Amount =Rs.2x, Rate =10%p.a.

S.I.=Rs.2x−Rs.x=Rs.x

∴ Time = x×10

x×100 =10 years.

Answer 2

The rate of interest is 40%.

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Let's understand a few concepts:

To calculate the simple interest we will use the following formula:

$\boxed{\bold{S.I. = \frac{Principal \times Rate \times Time }{100} }}$

To calculate the amount in simple interest we will use the following formula:

$\boxed{\bold{Amount = Principal + S.I.}}$

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Let's now solve the given problem:

Let "P" be the sum of money i.e., Principal.

∴ The amount after 20 years becomes = 9P

The no. of years i.e., Time = 20 years

Also, let the rate of interest be "R"%.

By combining the above formulas of simple interest, we can form an equation as,

$Amount - Principal = \frac{Principal \times Rate \times Time }{100}$

$\implies 9P - P = \frac{P \times R \times 20}{100}$

$\implies 8P = \frac{P \times R \times 1}{5}$

$\implies 8 = \frac{ R \times 1}{5}$

$\implies R = 8 \times 5$

$\implies \bold{R = 40\%}$

Thus, the rate of interest is 40%.

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