Question

2) The simple Interest on a certain sum computes to ₹600
in 3 years , and the compound interest on the same sum
at the same rate and for 2years compates to ₹410.
find the rate percent
can anyone pls this fast.
first to answer will be marked as the brainliest​

Answer 1

Answer:

Step 1:

Simple Interest, S.I. = Rs. 600

Time = 3 years

Let the rate of interest be “R” %.

We have,

S.I. = $\frac{P*R*T}{100}$  

Or, P = (600 * 100) / (R * 3)  ……. (i)

Step 2:

Compound interest, C.I. = Rs. 410

Time = 2 years

We know,  

C.I. = P [{1 + $\frac{R}{100}$}ⁿ - 1]

Since the P and R is the same for compound interest, therefore, substituting the value of P from (i), we get  

Or, 410 = [(600 * 100) / (R * 3)]  [{1 + (R/100)² - 1]

Or, 0.0205 R = [1² + 2R/100 + (R/100)²] - 1

Or, 0.0205 R = 0.02R + (R/100)²

Or, 0.0005 R = (R/100)²

Or, R = 0.0005 * 10000 = 5 %

Thus, the rate of interest is 5%.

Answer 2

Step 1:

Simple Interest, S.I. = Rs. 600

Time = 3 years

Let the rate of interest be “R” %.

We have,

S.I. = \frac{P*R*T}{100}

100

P∗R∗T

Or, P = (600 * 100) / (R * 3) ……. (i)

Step 2:

Compound interest, C.I. = Rs. 410

Time = 2 years

We know,

C.I. = P [{1 + \frac{R}{100}

100

R

}ⁿ - 1]

Since the P and R is the same for compound interest, therefore, substituting the value of P from (i), we get

Or, 410 = [(600 * 100) / (R * 3)] [{1 + (R/100)² - 1]

Or, 0.0205 R = [1² + 2R/100 + (R/100)²] - 1

Or, 0.0205 R = 0.02R + (R/100)²

Or, 0.0005 R = (R/100)²

Or, R = 0.0005 * 10000 = 5 %

Thus, the rate of interest is 5%.