yash invest 1200 in scheme A ,which offers a compd interest at rate of 20% for 2 yrs.he invested a certain sum in scheme B which offers simple interest at rate of 15 % for a period of 3 year. interest received from scheme A Is 42rs more than that received from scheme B.the sum invested in scheme B was what % of that?
If the amounts invested are a and b, we are told that
1200(1.20)^2 = b(1+.15*3) + 42
b = 1162.76
Now you ask what percent is B of "that". No idea what you mean, but if you want the percent of the total amount invested, that would be
b/(a+b) = 1162.76/2362.76 = .4921 = 49.21% of the total.
Let's solve this step-by-step:
Step 1: Calculate the interest earned from Scheme A.
Principal amount invested in Scheme A = Rs. 1200
Rate of interest = 20%
Time = 2 years
Using the formula for compound interest:
A = P(1 + r/n)^(nt), where:
A = Total amount after interest
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Time in years
A = 1200(1 + 0.20/1)^(1*2)
A = 1200(1 + 0.20)^2
A = 1200 * (1.20)^2
A = 1200 * 1.44
A = Rs. 1728
Interest earned from Scheme A = A - P
Interest earned from Scheme A = 1728 - 1200
Interest earned from Scheme A = Rs. 528
Step 2: Calculate the interest earned from Scheme B.
Rate of interest = 15%
Time = 3 years
Using the formula for simple interest:
SI = (P * r * t) / 100, where:
SI = Simple Interest
P = Principal amount
r = Rate of interest
t = Time in years
SI = (P * 15 * 3) / 100
SI = (P * 45) / 100
SI = 45P / 100
Step 3: Calculate the difference in interest between Scheme A and Scheme B.
Scheme A interest - Scheme B interest = 42
528 - (45P / 100) = 42
Step 4: Solve the equation for P (the sum invested in Scheme B).
486 = (45P / 100)
Multiplying both sides by 100:
48600 = 45P
Dividing both sides by 45:
P = 1080
Step 5: Calculate the percentage of the sum invested in Scheme B in relation to the sum invested in Scheme A.
(P / 1200) * 100 = (1080 / 1200) * 100 = 90%
Therefore, the sum invested in Scheme B was 90% of the sum invested in Scheme A.
To find the amount invested in scheme B as a percentage of scheme A, we need to follow these steps:
Step 1: Calculate the interest received from scheme A.
The formula to calculate the compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Number of years
In this case, the principal amount (P) is 1200, the annual interest rate (r) is 20% (or 0.2), and the number of years (t) is 2. Let's calculate the final amount (A) for scheme A.
A = 1200(1 + 0.2/1)^(1*2)
A = 1200(1 + 0.2)^2
A = 1200(1.2)^2
A = 1200(1.44)
A = 1728
The interest received from scheme A can be calculated by subtracting the principal amount from the final amount:
Interest from A = A - P
Interest from A = 1728 - 1200
Interest from A = 528
Step 2: Calculate the interest received from scheme B.
The formula to calculate the simple interest is:
I = P * r * t
Where:
I = Simple interest
P = Principal amount
r = Annual interest rate (in decimal form)
t = Number of years
In this case, the annual interest rate (r) is 15% (or 0.15), and the number of years (t) is 3. Let's calculate the interest received from scheme B.
Interest from B = P * r * t
528 = P * 0.15 * 3
528 = 0.45P
P = 528 / 0.45
P = 1173.33 (approximately)
Now we have the amount invested in scheme B, which is approximately 1173.33.
Step 3: Calculate the percentage.
To find the percentage of scheme B with respect to scheme A, we can use the formula:
Percentage = (Amount in Scheme B / Amount in Scheme A) * 100
Percentage = (1173.33 / 1200) * 100
Percentage = 97.77% (approximately)
Therefore, the sum invested in scheme B was approximately 97.77% of the sum invested in scheme A.