Simple Interest Ratio Calculation: A to B
The problem asks for the ratio of two sums, A and B, based on conditions involving simple interest.
Understanding Simple Interest
The formula for Simple Interest (SI) is:
$SI = (Principal × Rate × Time) / 100$Where:
- Principal is the sum of money (e.g., A or B).
- Rate is the annual interest rate (in percent).
- Time is the duration in years.
Calculating Simple Interest for Sum A
Principal = Rs. A
Rate = 6% per annum
Time = 2 years
Using the formula:
$SI_A = (A × 6 × 2) / 100$ $SI_A = (12A) / 100$Calculating Simple Interest for Sum B
Principal = Rs. B
Rate = 4% per annum
Time = 3 years
Using the formula:
$SI_B = (B × 4 × 3) / 100$ $SI_B = (12B) / 100$Equating the Simple Interests
The problem states that the simple interest for A is equal to the simple interest for B:
$SI_A = SI_B$Substituting the calculated values:
$(12A) / 100 = (12B) / 100$Determining the Ratio A:B
To find the ratio A:B, we can solve the equation:
Multiply both sides by 100:
$12A = 12B$Divide both sides by 12:
$A = B$Now, rearrange to find the ratio A/B:
$A / B = 1 / 1$Therefore, the ratio of A to B (A:B) is 1:1.
Similar Questions
- A sum doubles in 5 years at simple interest. What is the annual rate?
- A certain sum becomes 4 times itself in 8 years at simple interest. In how many years will it become 12 times itself at the same rate?
- If the simple interest on a certain sum of money for 4 years at 5% per annum is ₹500, what would be the simple interest on the same sum for 6 years at 7% per annum?
- If $P = \text{Rs. } 1500$, $R = 8.5\%$, and $T = 2.5 \text{ years}$, find the simple interest.
- A donor deposits ₹8,00,000 in a trust that earns 10% simple interest annually. The interest is used to distribute three annual awards. If the second and third awards are ₹35,000 and ₹20,000 respectively, what is the value of the first award?
- Rs. $1500$ is lent out at $6\%$ per annum simple interest for $3$ years. Find the amount after $3$ years.
- A sum amounts to ₹6,600 in 2 years and ₹7,200 in 4 years at simple interest. What is the rate of interest per annum?
A sum of ₹8000 is lent out in two parts, one at 5% simple interest and the other at 7% simple interest. If the annual interest is ₹500, the sum lent at 7% is:
What will the ratio be of the simple interest earned on a given amount at the same interest rate over 6 years compared to that earned over 9 years?
Pranav borrows a sum of ₹6,23,305 at the rate of 10% per annum simple interest. At the end of the first year, he repays ₹16,390 towards return of principal amount borrowed. If Pranav clears all pending dues at the end of the second year, including interest payment that accrued during the first year, how much does he pay (in ₹) at the end of the second year?
Important Questions from Simple Interest
If ₹12,800 is invested in a bank for 5 years at the rate of 9% per annum simple interest. what amount is returned by the bank?
Somu has borrowed ₹10,000 from a money lender with simple interest at a rate of 7% half yearly. How much amount will he pay to the money lender after 3 years?
Find the Simple interest on Rs. 2,400 from 20 March 2019 to 31 may 2019 at \(6{1 \over 4}\) % rate?
If the simple interest for five years is equal is 35% of the principal, that rate of interest is:
A sum fetched a simple interest of Rs. 3,040 at the rate of 8% p.a in 5 years. what is the sum?
