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- Find the simple interest (in ₹) on ₹4,000 at 6.75% per annum rate of interest deposited on 21 February 2024 and withdrawn on 22 April 2024.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 ₹).
- A sum of ₹800 becomes ₹920 in 3 years at simple interest. If interest is increased by 4%, then the amount will increase to:
- An amount becomes eight-fifth of the original amount in 5 years at what percentage rate of simple interest per annum?
- The rate at which a sum becomes 2 times of itself in 10 years at simple interest is:
- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 4 February 2024 and withdrawn on 5 April 2024.
- How many years will it take for an amount of ₹400 to yield ₹450 as interest at 5% per annum on simple interest?
- Vikas took a loan of ₹1,200 on simple interest that is equal to as many years as the rate of interest. If he paid ₹768 as interest at the end of the loan period, then what was the rate of interest?
- A sum of money amounts to ₹12,000 after 6 years and ₹15,000 after 9 years at the same rate of simple interest. What is the rate of interest per annum?
- What will be the amount of simple interest on ₹75,000 at the rate of $2\frac{5}{3}\%$ per annum for a period of 5 years?
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?
