To find the value of the first award, we need to calculate the total annual simple interest earned and then determine how the awards are distributed based on this interest.
Calculate Annual Simple Interest
The formula for simple interest is:
$ \text{Simple Interest} (SI) = \frac{P \times R \times T}{100} $
Where:
- Principal (P) = ₹8,00,000
- Rate (R) = 10% per annum
- Time (T) = 1 year (since interest is calculated annually for distribution)
Substituting the values:
$ SI = \frac{800000 \times 10 \times 1}{100} $
$ SI = ₹80,000 $
The trust earns ₹80,000 in simple interest annually.
Determine Award Distribution
The problem states that "The interest is used to distribute three annual awards." The most logical interpretation that fits the options is that the sum of all three awards equals the total annual interest earned.
Let the three awards be A1, A2, and A3.
$ \text{Total Interest} = A1 + A2 + A3 $
We know:
- Total Annual Interest = ₹80,000
- Second Award (A2) = ₹35,000
- Third Award (A3) = ₹20,000
Calculate the First Award (A1)
Substitute the known values into the equation:
$ ₹80,000 = A1 + ₹35,000 + ₹20,000 $
First, sum the known awards:
$ ₹35,000 + ₹20,000 = ₹55,000 $
Now, solve for A1:
$ ₹80,000 = A1 + ₹55,000 $
$ A1 = ₹80,000 - ₹55,000 $
$ A1 = ₹25,000 $
The value of the first award is ₹25,000.
Similar Questions
- If the simple interest on a sum of Rs. A at 6% per annum for 2 years is equal to the simple interest on Rs. B at 4% per annum for 3 years, then what is the ratio of A to B?
- 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.
- 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?
