A lent Rs. 25000 to B and at the same time lent some amount to C at the same 7% simple interest. After 4 years a received Rs. 11200 as interest from B and C. How much did A lend to C?
Rs. 15000
Understanding the Simple Interest Problem
This question asks us to find the amount of money A lent to C, given information about two simple interest loans made by A to B and C. We know the principal lent to B, the interest rate, the time period, and the total interest received from both B and C.
Key Concepts: Simple Interest
Simple interest is calculated only on the principal amount. The formula for simple interest (SI) is:
\( \text{SI} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100} \)
Where:
- P is the principal amount (the initial amount borrowed or lent).
- R is the annual interest rate (in percent).
- T is the time period (in years).
Step-by-Step Solution for the Loans
Loan to B: Calculating Interest from B
First, let's calculate the simple interest received from B. We are given:
- Principal lent to B (PB) = Rs. 25000
- Interest Rate (R) = 7% per annum
- Time Period (T) = 4 years
Using the simple interest formula:
\( \text{SI}_B = \frac{P_B \times R \times T}{100} \)
\( \text{SI}_B = \frac{25000 \times 7 \times 4}{100} \)
\( \text{SI}_B = \frac{25000 \times 28}{100} \)
\( \text{SI}_B = 250 \times 28 \)
\( \text{SI}_B = 7000 \)
So, the simple interest received from B is Rs. 7000.
Loan to C: Setting up the Equation for Unknown Principal
Now, let's consider the loan to C. We are given:
- Principal lent to C (PC) = Unknown (let's call it \(P_C\))
- Interest Rate (R) = 7% per annum (same as B)
- Time Period (T) = 4 years (same as B)
The simple interest from C is:
\( \text{SI}_C = \frac{P_C \times R \times T}{100} \)
\( \text{SI}_C = \frac{P_C \times 7 \times 4}{100} \)
\( \text{SI}_C = \frac{P_C \times 28}{100} \)
Using the Total Interest Information
The question states that A received a total of Rs. 11200 as interest from B and C. This means:
\( \text{Total Interest} = \text{SI}_B + \text{SI}_C \)
\( 11200 = 7000 + \text{SI}_C \)
Now we can find the interest received from C:
\( \text{SI}_C = 11200 - 7000 \)
\( \text{SI}_C = 4200 \)
The simple interest received from C is Rs. 4200.
Finding the Principal Lent to C
We know the simple interest from C (\(\text{SI}_C\)), the rate (R), and the time (T). We can use the simple interest formula to find the principal lent to C (\(P_C\)):
\( \text{SI}_C = \frac{P_C \times R \times T}{100} \)
Substitute the known values:
\( 4200 = \frac{P_C \times 7 \times 4}{100} \)
\( 4200 = \frac{P_C \times 28}{100} \)
To solve for \(P_C\), we can rearrange the equation:
\( P_C = \frac{4200 \times 100}{28} \)
\( P_C = \frac{420000}{28} \)
Let's perform the division:
| Division | Result |
|---|---|
| \(420000 \div 28\) | 15000 |
\( P_C = 15000 \)
Therefore, the amount A lent to C was Rs. 15000.
Conclusion
By calculating the simple interest from the known loan (to B) and subtracting it from the total interest received, we found the interest from the unknown loan (to C). Using the simple interest formula again with the interest from C, the rate, and the time, we were able to determine the principal amount lent to C.
Revision Table: Simple Interest Calculation
| Item | Value for Loan to B | Value for Loan to C |
|---|---|---|
| Principal (P) | Rs. 25000 | \(P_C\) (Unknown) |
| Rate (R) | 7% | 7% |
| Time (T) | 4 years | 4 years |
| Simple Interest (SI) | SIB = Rs. 7000 (Calculated) | SIC = Rs. 4200 (Calculated from Total) |
| Total Interest (SIB + SIC) | Rs. 11200 (Given) | |
Additional Information: Simple vs. Compound Interest
It's important to distinguish simple interest from compound interest.
- Simple Interest: Interest is calculated only on the initial principal amount. The principal remains constant throughout the loan period. The interest earned does not earn further interest.
- Compound Interest: Interest is calculated on the initial principal and also on the accumulated interest from previous periods. The principal effectively grows over time as interest is added to it, leading to faster growth of the total amount.
The formula for the Amount (A) with compound interest is:
\( A = P \left(1 + \frac{R}{100}\right)^T \)
Where P is principal, R is annual rate, and T is time in years. Compound interest problems require a different calculation method.
In this problem, the term "simple interest" is clearly stated, so we use the simple interest formula.
Similar Questions
If a sum of money at a certain rate of simple interest per year doubles in 5 years and at a different rate of simple interest per year becomes three times in 12 years, then the difference in the two rates of simple interest per year is
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Two equal amounts were borrowed at 5% and 4% simple interest. The total interest after 4 years amounted to Rs. 405. What was the total amount borrowed?
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A person divided a sum of Rs. 17, 200 into three parts and invested at 5%, 6% and 9% per annum simple interest. At the end of two years, he got the same interest on each part of money. What is the money invested at 9%?
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Important Questions from Simple Interest
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
Nirav and Mehul borrowed Rs.4000 and Rs.5000 respectively for 2.5 years at the rate of x% per annum. Mehul paid Rs 125 more interest than Nirav. Find x.
If the interest on a sum of Rs.1200 is more than the interest on Rs.1000 by Rs.120 in three years, then what is the rate of interest per annum?.
The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2.50. What is the difference between their rates?
A sum of Rs.1200 becomes Rs.1560 at a rate of simple interest in 3 years. In how many years will the sum of Rs.800 amount to Rs.1120 at the same rate of simple interest?
