Question

a sum of money becomes 16/5 times itself in 22 years at R% p.a. simple interest. what is value of R?

Answer 1

Answer:

10

Step-by-step explanation:

T=22

(16p-p)/5

11p/5

(p*r*t)/100

10

Answer 2

The value of R is 10% p.a.simple interest.

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Let's understand a few concepts:

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

$\boxed{\bold{Simple\:Interest = \frac{Principal \times Rate \times Time}{100} }}$

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

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

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Let's solve the given problem:

Let,

"P" → represents the sum of money (Principal)

"R" → represents the rate of simple interest

∴ The amount will be = 16/5 of principal = $\frac{16}{5} P$

The no. of years (T) = 2 years

By combining both the formula above, we can form an equation as,

$Amount - P = \frac{P\times R \times T}{100}$

$\implies \frac{16}{5}P - P = \frac{P\times R \times 22}{100}$

$\implies \frac{16 - 5}{5}P = \frac{P\times R \times 22}{100}$

$\implies \frac{11}{5}P = \frac{P\times R \times 22}{100}$

$\implies \frac{11}{5} = \frac{ R \times 22}{100}$

$\implies R = \frac{11 \times 100}{5\times 22}$

$\implies \bold{R = 10\%}$

Thus, the value of R is 10%.

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