Question

7. A sum of money becomes 3250 in 3 years and 3875 in 5 years 6 months at a simple
interest per annum. Find the principal and the rate of interest.?
​

Answer 1

Answer:

The sum is Rs. 2500 and rate of interest is 6%.

Step-by-step explanation:

Given:

Amount in 2 years = Rs. 2800

Amount in 5 years = Rs. 3250

To find: Principal and rate of interest.

We know that,

SI=\frac{P\times R\times T}{100}SI=

100

P×R×T

A = P + SI

SI = A - P

let, P be the principal and R is the rate of interest.

According to the Question,

2800-P=\frac{P\times R\times2}{100}2800−P=

100

P×R×2

140000 - 50P = PR ............................(1)

3250-P=\frac{P\times R\times5}{100}3250−P=

100

P×R×5

65000 - 20P = PR ............................(2)

Divide (2) by (1),

\frac{140000-50P}{65000-20P}=\frac{PR}{PR}

65000−20P

140000−50P

=

PR

PR

140000 - 50P = 65000 - 20P

50P - 20P = 140000 - 65000

30P = 75000

P = 2500

Put this value of P in (1),

140000 - 50(2500) = 2500R

2500R = 140000 - 125000

2500R = 15000

R = 6

Therefore, The sum is Rs. 2500 and rate of interest is 6%.

Answer 2

The Principal and the rate of Interest are Rs.2500 and 10% respectively.

Given:-

Amount in Case 1 = Rs.3250

Time in Case 1 = 3years

Amount in Case 2 = Rs.3875

Time in Case 2 = 5years 6 months

To Find:-

The Principal and the rate of Interest.

Solution:-

We can easily find out the value of Principal and the rate of Interes by using these simple steps.

As

Amount in Case 1 = Rs.3250

Time in Case 1 = 3years

Amount in Case 2 = Rs.3875

Time in Case 2 = 5years 6 months

Difference in time = 2years 6 months

Difference in Amount = Rs.625

Annual Interest (AI) =?

According to the formula of Annual Interest,

$AI = \frac{∆ \: amount}{∆ \: time}$

$AI = \frac{625}{2.5}$

$AI = \frac{6250}{25}$

$AI = 250$

Principal Amount = Amount in Case 1 - Annual Interest×time

PA = A + (AI×T)

Principal Amount= 3250 - 250 × 3

PA = 3250 - 750

PA = 2500

Now, Rate of Interest (r) =?

Rate of interest is given by the formula,

$r = \frac{AI}{amount} \times 100$

$r = \frac{250}{2500} \times 100$

$r = \frac{25000}{2500}$

$r = 10\%$

Hence, The Principal and the rate of Interest are Rs.2500 and 10% respectively.

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