A sum of money would amount to Rs.6,200 in 2 years and Rs.7,400 in 3 years.The principal and rate of simple interest are:
A sum of money would amount to Rs.6,200 in 2 years and Rs.7,400 in 3 years.
The principal and rate of simple interest are:
KINDLY GIVE SOLUTION
What answer sir
To find the principal and the rate of simple interest, we can use the formula for finding the amount of money with simple interest:
A = P(1 + rt)
Where:
A = Amount of money after a certain period of time
P = Principal (the initial sum of money)
r = Rate of interest per year
t = Time in years
From the given information, we have:
A1 = Rs.6,200 after 2 years
A2 = Rs.7,400 after 3 years
Using the formula, we can set up two equations:
A1 = P(1 + r * 2) (equation 1)
A2 = P(1 + r * 3) (equation 2)
Substituting the given values:
6200 = P(1 + 2r) (equation 1)
7400 = P(1 + 3r) (equation 2)
Now we have a system of two equations with two unknowns (P and r). We can solve this system using various methods such as substitution or elimination. Let's use the substitution method:
From equation 1, we can rearrange it to solve for P:
P = 6200 / (1 + 2r)
Now we substitute this value of P in equation 2:
7400 = (6200 / (1 + 2r)) * (1 + 3r)
Simplifying further:
7400 = 6200 + 18600r / (1 + 2r)
Multiplying both sides by (1 + 2r):
7400(1 + 2r) = 6200 + 18600r
Distributing and rearranging:
7400 + 14800r = 6200 + 18600r
Subtracting 14800r from both sides:
7400 - 6200 = 18600r - 14800r
1200 = 3800r
Dividing both sides by 3800:
r = 1200 / 3800
Simplifying:
r ≈ 0.3158
Now, substitute this value of r in equation 1:
6200 = P(1 + 2 * 0.3158)
6200 = P(1 + 0.6316)
6200 = P * 1.6316
Dividing both sides by 1.6316:
P ≈ 3799.88
Therefore, the principal (P) is approximately Rs.3799.88 and the rate of interest (r) is approximately 0.3158.