Question

a sum of Lent out at simple interest becomes 4480 rs in three year and 4800 in 5 years find the rate of interest?​

Answer 1

Answer:

Step-by-step explanation:

Hope you understand. .

Answer 2

The rate of interest is 4%.

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Let's understand a few concepts:

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

$\boxed{\bold{Simple\:Interest = \frac{Principal(P)\times Rate(R)\times Time(T)}{100} }}$

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

$\boxed{\bold{Amount (A)= Principal (P)+ S.imple\:Interest(S.I.)}}$

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Let's now solve the given problem:

Let's say,

"P" → the sum of money i.e., Principal.

"R" → the rate of interest

For 3-year Simple Interest:

The amount received at the end of 3 years i.e., A = Rs. 4480

The no. of years i.e., T = 3 years

By using the above two formulas of simple interest, we get,

$A - P = \frac{PRT}{100}$

$\implies 4480 - P = \frac{P R \times 3}{100}$

$\implies 100(4480 - P) = 3PR$

$\implies 448000 - 100P = 3PR\:.\:.\:.\:(1)$

For 5-year Simple Interest:

The amount received at the end of 5 years i.e., A = Rs. 4800

The no. of years i.e., T = 5 years

By using the above two formulas of simple interest, we get,

$A - P = \frac{PRT}{100}$

$\implies 4800- P = \frac{P R \times 5}{100}$

$\implies 100(4800 - P) = 5PR$

$\implies 20(4800 - P) = PR$

$\implies 96000 - 20P = PR\:.\:.\:.\:(2)$

On substituting equation (2) in (1), we get

$448000 - 100P = 3(96000 - 20P )$

$\implies 448000 - 100P = 288000 - 60P$

$\implies 448000 - 288000 = 100 P - 60P$

$\implies 16000 =40P$

$\implies P = 4000$

On substituting the value of P = 4000 in equation (1), we get

$448000 - (100\times 4000) = (3\times 4000)R$

$\implies 448000 - 400000 = 12000\times R$

$\implies 48000 = 12000\times R$

$\implies \bold{R = 4\%}$

Thus, the rate of interest is 4%.

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