Simple Interest Calculation: Profit Analysis
The problem describes a scenario with two related simple interest transactions. We need to find the initial principal amount based on the profit earned by Arif.
- Kumar lends a principal amount (P) to Arif at 10% simple interest per year for 3 years.
- Arif then lends this same principal amount (P) to Naresh at 20% simple interest per year for 3 years.
- Arif's net gain (profit) from these transactions is ₹1,560 over the 3 years.
Interest Calculations
Let the principal amount lent by Kumar to Arif be '$P$'.
- The interest rate for the loan from Kumar to Arif is $R_1 = 10\%$ p.a.
- The interest rate for the loan from Arif to Naresh is $R_2 = 20\%$ p.a.
- The time period for both loans is $T = 3$ years.
The formula for Simple Interest (SI) is given by:
$SI = \frac{P \times R \times T}{100}$Calculate the interest Arif pays to Kumar:
$SI_{paid} = \frac{P \times 10 \times 3}{100} = \frac{30P}{100}$Calculate the interest Arif receives from Naresh:
$SI_{received} = \frac{P \times 20 \times 3}{100} = \frac{60P}{100}$Principal Amount Determination
Arif's profit is the difference between the interest he received and the interest he paid:
$Profit = SI_{received} - SI_{paid}$We are given that Arif's profit is ₹1,560:
$\frac{60P}{100} - \frac{30P}{100} = 1560$Combine the terms:
$\frac{(60 - 30)P}{100} = 1560$ $\frac{30P}{100} = 1560$To find the principal amount $P$, rearrange the equation:
$0.30 \times P = 1560$ $P = \frac{1560}{0.30}$ $P = \frac{15600}{3}$ $P = 5200$The amount that Kumar lent to Arif was ₹5,200.
Similar Questions
- Find the simple interest (in ₹) on ₹4,000 at 6.75% per annum rate of interest deposited on 21 February 2024 and withdrawn on 22 April 2024.
- Sapna invested ₹21,900 on simple interest, partly at 14% per annum and partly at 10% per annum. If she earns equal interests from the two investments after 2 years, then find the sum invested at 14% per annum (in ₹).
- Find the simple interest (in ₹) on ₹1,200 at an interest rate of 4% per month for 11 months.
- A man purchases a washing machine for $₹12,000$. He pays $₹2,000$ at first and the rest after $1\text{ year}$, on which he is charged a simple interest at the rate of $10\%$ per year. The total amount he pays for the washing machine is:
- Sapna invested ₹21,700 on simple interest, partly at 3% per annum and partly at 12% per annum. If she earns equal interests from the two investments after 7 years, then find the sum invested at 3% per annum (in ₹).
- A sum of ₹800 becomes ₹920 in 3 years at simple interest. If interest is increased by 4%, then the amount will increase to:
- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 4 February 2024 and withdrawn on 5 April 2024.
- Sapna invested ₹20,300 on simple interest, partly at the rate of 8% per annum and partly at the rate of 6% per annum. If she earns equal interests from the two investments after 6 years, then find the sum invested at the rate of 8% per annum (in ₹).
- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 5 February 2024 and withdrawn on 6 April 2024.
- What sum of money (in ₹) will amount to ₹2,400 at 5% per annum simple interest in 4 years?
Important Questions from Simple Interest
Anil lent a sum of Rs. 5,000 on simple interest for 10 years in such a way that the rate of interest is 6% per annum for the first 2 years, 8% per anmum for the next 2 years and 10% per annum beyond 4 years. How much interest (in Rs.) will he earn at the end of 10 years?
What will be the simple interest on a sum of Rs. 12000 at the rate of 15 percent per annum for three years ?
If in 13 years fixed sum doubles at simple interest, what will be the interest rate per year? (correct to two decimal places)
On simple interest a sum of Rs. 640 becomes Rs. 832 in 2 years. What will Rs. 860 become in 4 years at the same rate of simple interest?
A certain sum amounts to Rs. 81840 in 3 years and to Rs. 92400 in 5 years at x% p.a. under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?
