Question

A Sum of money amount to *2600 in 3 years and to 2900 in 4.5 years at simple interest. Find the sum and rate of interest.​

Answer 1

Answer:

Step-by-step explanation:

Given, P= Rs 2000, A= Rs 2600, T=5 years

∴ S.I.=A−P= Rs 2600− Rs 2000 = Rs 600

R =  

P×T

S.I.×100

​

=  

2000×5

600×100

​

=6% per annum

Now, P= Rs 2000, T=5 years,

R=(6+3)%p.a.=9% per annum

∴ A=P+  

100

P×R×T

​

 

= Rs 2000 + Rs  

100

2000×9×5

​

 

= Rs 2000 + Rs 900 = Rs 2900

Answer 2

The sum is Rs. 2000.

The rate of interest is 10% p.a..

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Let's understand a few concepts:

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

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

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's say,

"P" → represents the principal

"R" → represents the rate of interest

When Amount = Rs. 2600 and Time = 3 years, by combining the above two formulas we get,

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

$\implies 2600 - P = \frac{P \times R \times 3}{100}$

$\implies 260000 - 100 P = 3P R$ . . . (1)

When Amount = Rs. 2900 and Time = 4.5 years, by combining the above two formulas we get,

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

$\implies 2900 - P = \frac{P \times R \times 4.5}{100}$

$\implies 290000 - 100 P = 4.5P R$ . . . (2)

By subtraction equation (1) from (2), we get

$290000 - 100 P = 4.5P R\\260000 - 100 P = 3P R\\- \:\:\:\:\:\:\:\:\: + \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:-\:\:\\\ ----------- \\ 30000 \:=\:1.5PR\\ -----------$

∴ $PR = 20000$ . . . (3)

On substituting equation (3) in (1), we get

$260000 - 100 P = 3\times 20000$

$\implies 260000 - 100 P = 60000$

$\implies 100 P = 260000 - 60000$

$\implies 100 P = 200000$

$\implies \bold{P = Rs.\:2000}$ ← the sum

On substituting P = 2000 in (3), we get

$2000\times R = 20000$

$\implies R = \frac{20000}{2000}$

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

Thus,

The sum is Rs. 2000.

The rate of interest is 10% p.a..

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