How to Solve Simple Interest Problems for NID

Simple interest is interest calculated on the principal portion of a loan or the original contribution to a saving account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.

It is a sum which is paid by the borrower to the lender for using the money for a specific period of time. The money borrowed is the principal.

The rate at which the interest is calculated on the principal is called the rate of interest. The time for which the money is borrowed is the time and the total sum of principal and interest is called amount.

Simple Interest is the interest calculated on the original principal at any rate of interest for any period of time, then it is called simple interest.

If P = Principal, 

R = Rate percent per annum,

T = Number of years,

SI = Simple Interest and

A = Amount 

Then,

73 days = ⅕ yr

146 days = ⅖ yr

219 days = ⅗ yr

292 days = ⅘ yr

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The formula of simple interest is:

Simple Interest = Principal x Time Period x Rate of Interest / 100

Principal = 100 x Simple Interest / Rate of Interest x Time period

Rate of Interest = 100 x Simple Interest / Principal x Time Period

Time = 100 x Simple Interest / Principal x Rate of Interest

Amount = Principal x Simple Interest

Here, the interest is calculated on the original principal, i.e., the principal, to calculate the interest it remains constant throughout the time period. The interest earned on the principal is not taken into account for the purpose of calculating interest for later years.

In this article, you will get to know how to solve simple interest problems for NID.

Tricks to Solve Simple Interest Problems for NID

The key to success in the exam is planning a well-structured study plan for NID and executing it effectively.

Before solving the simple interest problems for NID we should know all the parameters which will help in solving simple interest problems.

• Whenever a certain amount is borrowed, lent, credited or debited or invested some sort of these terms are used in a question related to simple interest then you need to understand that this money is going to be considered as principal amount.
• Whenever this amount is borrowed or lent, this money is given at a certain rate of interest but if in the question it is not mentioned then we have to consider the rate of interest annually only. The rate of interest will be denoted as capital ‘R’.
• Whenever you are borrowing or lending money then you will get the Time to return or get return back that money with interest. That time period is considered as Time and is denoted with capital ‘T’
• Whenever you are solving the simple interest questions then you have to know how to convert percentage to fraction form that will make it easy for you to solve the question.

The fractional value of 25% is ¼, the fractional value of 20% is ⅕, and the fractional value of 33.33% is ⅓. 

For example: In a question the rate of interest is given as 8.33% per annum so it will be 1/12 in the fractional form. Here that 1/12 means that 12 the denominator is the principal amount and 1 the numerator is the interest when you have received or paid on the principal amount in one year.

To help you get an idea about the type of questions asked in the exam, we have curated few sample questions from the previous year's NID Question papers.

Let us understand with an example:

For example 1: Sagar borrows Rs. 50,000 from a bank for 5 years. What is the rate of simple interest charged by the bank if after 5 years Sagar had to pay Rs. 66,000 to the bank?  

Answer: 6.4 %

Solution:

This question can be solved in a fraction of seconds by using the simple interest formula but we will solve it by a different method so that you can easily understand the simple interest concept.

Once you have understood the simple interest concept you can easily solve any kind of question related to simple interest in seconds.

To given: sagar has borrowed rs. 50,000 from a bank for 5 years

And, after 5 years, Sagar will pay rs. 66,000 to the bank.

To find: the rate of interest on which sagar had borrowed the money from bank

Let us find out,

Sagar had borrowed Rs. 50,000 and he has to pay Rs. 66,000 after 5 years

So,

In this case we can say that the additional amount which sagar is paying is our simple interest

So, we will see the additional amount by subtracting Rs. 50,000 from Rs. 66,000.

The additional amount which he will pay as a simple interest will be 66,000 - 50,000 = 16,000.

So, the simple interest for 5 years will be Rs. 16,000

 Now, we have to find at what rate of interest per annum he is paying the interest to the bank

So, the total simple interest for 5 years is Rs. 16,000

So the simple interest for 1 year will be 16000/5 = 3,200

Rate of interest = simple interest is what percentage of principal per year

Now, see below

Simple interest = Rs. 3,200 for 1 year

Principal amount = Rs. 50,000

Rate of interest = simple interest of 1 year / principal amount * 100

Rate of interest = 3200 / 50000 x 100

Rate of interest = 6.4 %

So, the rate of interest on which sagar will pay the interest to the bank every year will be 6.4%

Let us understand the concept more by solving one more example

For Example 2:

After how many years would an amount double itself at 15% rate of simple interest?

Answer: in 7 years approximately the invested amount will be doubled.

Explanation:

To given: rate of simple interest 15%

To find: In what time the principal amount will be doubled..

Solution: 

First we will convert percentage into fraction

So,

5% = 1/20

10% = 1/10

15% = 3/20

When you have converted percentage into fraction

It means 

That 15% = 3 / 20 

As we have mentioned above, if the rate of interest is given in percentage and we have converted that into a fraction then the numerator will be assumed as the interest amount and the denominator will be assumed as the principal amount.

So, in this case

The rate of interest is 15 % which is 3 / 20.

So, this means that 3 is the interest amount and 20 will be the principal amount.

This means that if you have invested Rs. 20 then after 1 year you will get Rs. 3 as an interest earned.

So, now we have to find in what time the money which is invested will be doubled. Which means in what time you will get that much interest that will be equal to the invested money.

Now, we will calculate the time that in how many years the invested money is doubled.

⇒ Invested money = interest earned per annum X ‘n’ number of time

⇒ 20 = 3 x n

 ⇒ n = 20 / 3

⇒ n = 6.66 years

⇒ n = 7 years approx.

So, in 7 years the money invested will be doubled when the interest earned at a rate of 15% per annum.

These are some of the questions mentioned below to show you how you can solve simple interest questions for NID examination. These questions will help you to easily understand the format to solve the simple interest questions for NID examination.

By solving these questions you will find that the simple interest questions are easy to solve and very scoring. You will get every trick and method to solve simple interest questions easily. So practice these questions and enhance your preparation.

For more questions you can visit us at www.toprankers.com.

Question 1: Find the simple interest on Rs. 7,200 at 8% per annum for 10 months.

1. Rs. 480
2. Rs. 420
3. Rs. 450
4. Rs. 410
5. None of these

Answer: (a) Rs. 480

Explanation:

To Given: Principal amount - Rs. 7,200

Rate of interest = 8% per annum

Time = 10 months

To find: Simple Interest?

Solution: here principal = Rs. 7,200

Rate of interest = 8% per annum

Time = 10/12 years = ⅚ years

⇒ Simple Interest = (Principal x Time x Rate of Interest / 100)

⇒ SI = (P x T x R / 100)

⇒ Simple Interest = (7200 x ⅚ x 8 / 100)

⇒ Simple Interest = 60 x 8

⇒ Simple Interest = Rs. 480.

Therefore, the simple interest is Rs. 480. 

Question 2: Find the simple interest on Rs, 14,600 at 8 ¼ % per annum for the period from 10th March, 2009 to 17th June, 2009. 

1. Rs. 310
2. Rs. 320
3. Rs. 330
4. Rs. 340
5. None of these

Answer: (e) None of these

Explanation:

To given: principal amount = Rs. 14,600

Rate of interest = 8 ¼ %

Time = 10th March, 2009 to 17th June, 2009.

To find: Simple interest?

Solution: Here 

Principal amount = Rs. 14,600

Rate of interest = 8 ¼ % = 33/4 % per annum

Time = March + April + May + June 

⇒ Time = 21 days + 30 days + 31 days + 17 days 

⇒ Time = 99 days.

⇒ Simple Interest = (Principal x Time x Rate of Interest / 100)

⇒ SI = (P x T x R / 100)

⇒ Simple Interest = (14600 x 33/4 x 99/365 / 100)

⇒ Simple Interest = (14600 x 33/4 x 99/365 x 1/100)

⇒ Simple Interest = (146 x 33/4 x 99/365)

⇒ Simple Interest = Rs. 326.70

Therefore, the simple interest is Rs. 326.70

Question 3: Find the amount on a principal of Rs. 3,600 for 2 years and 9 months at a rate of 8 ⅓ % per annum. 

1. Rs. 5,175
2. Rs. 4,425
3. Rs. 5,425
4. Rs. 4,175
5. None of these

Answer: (b) Rs. 4,425

Explanation:

To Given: Principal amount = Rs. 3,600

Rate of Interest = 8 ⅓ % per annum

Time = 2 years and 9 months

To Find: Simple Interest and Total Amount

Solution: Here

Principal Amount = Rs. 3,600

Rate of Interest = 8 ⅓ % = 25/3 %

Time = 2 years and 9 months 

⇒ Time = (2 x 12) + 9 / 12 years

⇒ Time = 33/12 years

⇒ Time = 11/4 years

⇒ Simple Interest = (Principal x Time x Rate of interest / 100) 

⇒ SI = (P x T x R / 100)

⇒ Simple Interest = (3600 x 11/4 x 25/3 / 100)

⇒ Simple Interest = (3600 x 11/4 x 25/3 x 1/100)

⇒ Simple Interest = (36 x 11/4 x 25/3)

⇒ Simple Interest = (3 x 11 x 25)

⇒ Simple Interest = Rs. 825

Therefore, the Simple Interest is Rs. 825.

⇒ Total Amount to be paid = Principal Amount + Simple Interest

⇒ Total Amount to be paid = P + SI

⇒ Total amount to be paid = 3600 + 825

⇒ Total Amount to be paid = Rs. 4,425.

Therefore, the Total Amount to be paid is Rs. 4,425

Question 4: The simple interest earned on a certain sum is Rs. 1,560 at the rate 8% per annum in 2 years. Find the sum.

1. Rs. 9,630
2. Rs. 9.140
3. Rs. 9,750
4. Rs. 9,810
5. None of these

Answer: (c) Rs. 9750

Explanation: 

To Given: Simple Interest = Rs. 1,560

Rate of Interest = 8% per annum

Time = 2 years

To find: the sum or Principal Amount

Solution: Here

Simple Interest = Rs. 1,560

Rate of Interest = 8% per annum

Time = 2 years

Let the principal amount be 𝒙

⇒ Simple Interest = (Principal x Time x Rate of Interest / 100) 

⇒ Simple Interest = (P x T x R / 100)

⇒ 1560 = (𝒙 x 2 x 8/100)

⇒ 1560 = (𝒙 x 2 x 2/25)

⇒ 1560 = 4𝒙 / 25

⇒ 𝒙 = 1560 x 25 / 4

⇒ 𝒙 = 9750

Therefore, the Principal Amount = Rs. 9,750 

Question 5: A certain sum amounts to Rs. 7,080 in 2 years and to Rs. 8,430 in 4 ½ year at simple interest. Find the rate of interest.

1. 7%
2. 8%
3. 6%
4. 9%
5. None of these

Answer: (d) 9%

Explanation:

To given: Amount in 4 ½ years = Rs. 8,430

Amount in 2 years = Rs. 7,080

To Find: Rate of Interest?

Solution: Here

Amount in 4 ½ years = Rs. 8,430

Amount in 2 years = Rs. 7,080

First we will find simple interest for 2 ½ years

Then after calculating simple interest for 2 ½ years 

We will calculate simple interest for 2 years

⇒ Simple Interest for 2 ½ years = (Amount in 4 ½ years - Amount in 2 years)

⇒ Simple interest for 2 ½ years = (8430 - 7080)

⇒ Simple Interest for 2 ½ years = Rs. 1,350

⇒ Simple Interest for 2 years = (1350 x ⅖ x 2)

⇒ Simple Interest for 2 years = (270 x 4)

⇒ Simple Interest for 2 years = Rs.1,080

Now, we will find the principal amount.

⇒ Principal = (Amount in 2 years) - (Simple Interest for 2 years)

⇒ Principal = (7080) - (1080)

⇒ Principal = (7080 - 1080)

⇒ Principal = Rs. 6,000 

After calculating the Principal amount, 

we will calculate the rate of interest 

Now,

Principal = Rs. 6,000

Time = 2 years

Simple Interest = Rs. 1,080

⇒ Rate of Interest = (100 x Simple Interest / Principal x Time)

⇒ Rate of Interest = (100 x SI / P x T)

⇒ Rate of Interest = (100 x 1080 / 6000 x 2)

⇒ Rate of Interest = (108 / 12)

⇒ Rate of Interest = 9 % per annum.

Therefore, the rate of interest = 9 % per annum.

Question 6: At what rate will Rs. 14,400 give Rs. 4,032 as simple interest in 3 years and 6 months?

1. 8%
2. 9%
3. 8 ½ %
4. 9 ½ %
5. None of these

Answer: (a) 8%

Explanation:

To Given: Principal = Rs. 14,400

Time = 3 ½ years

Simple Interest = Rs. 4,032

To Find: Rate of interest per annum.

Solution: Here

Principal = Rs. 14,400

Simple Interest = Rs. 4,032

Time = 3 ½ years 

Rate of interest per annum = ?

⇒ Time = 3 ½ years 

⇒ Time = 7/2 years

Now, we will calculate the rate of interest per annum.

⇒ Rate of interest per annum = (100 x Simple Interest / Principal x Time)

⇒ R = (100 x SI / P x T)

⇒ Rate of Interest = (100 x 4032 / 14400 x ⅖)

⇒ Rate of Interest = (100 x 4032 x 2 / 14400 x 7)

⇒ Rate of Interest = (8064 / 1008)

⇒ Rate of Interest = 8 % per annum

Therefore, the rate of interest per annum = 8% 

Question 7: In what time will a sum double itself at 8% per annum simple interest?

1. 12 year
2. 10 year
3. 12 ½ year
4. 10 ½ year
5. None of these

Answer: (c) 12 ½ year

Explanation:

To given: Rate of simple interest is 8%

To find: In what time the principal amount will be doubled..

Solution: 

First we will convert percentage into fraction

So,

5% = 1/20

10% = 1/10

8% = 2/25

When you have converted percentage into fraction

It means 

That 8% = 2 / 25 

As we have mentioned above, if the rate of interest is given in percentage and we have converted that into a fraction then the numerator will be assumed as the interest amount and the denominator will be assumed as the principal amount.

So, in this case

The rate of interest is 8 % which is 2 / 25.

So, this means that 2 is the interest amount and 25 will be the principal amount.

This means that if you have invested Rs. 25 then after 1 year you will get Rs. 2 as an interest earned.

So, now we have to find in what time the money which is invested will be doubled. Which means in what time you will get that much interest that will be equal to the invested money.

Now, we will calculate the time that in how many years the invested money is doubled.

⇒ Invested money = interest earned per annum X ‘n’ number of time

⇒ 25 = 2 x n

 ⇒ n = 25 / 2

⇒ n = 12.5 years

⇒ n = 12 ½ years

So, in 12 ½ years the money invested will be doubled when the interest earned at a rate of 8% per annum.

OR 

We can calculate time by one more method i.e.

Let the sum be Rs. 100

It is given in the question that amount is double of the sum

So, 

Amount be Rs. 200

⇒ Simple Interest = Amount - Principal 

⇒ Simple Interest = 200 - 100

⇒ Simple Interest = Rs. 100

Now, 

⇒Time = (100 x Simple Interest / Principal x Rate of Interest)

⇒ Time = (100 x SI / P x R)

⇒ Time = (100 x 100 / 100 x 8)

⇒ Time = 100 / 8

⇒ Time = 25 / 2 years

⇒ Time = 12 ½ years

Therefore, in 12 ½ years the sum will be doubled itself.

Question 8: At what rate will a sum increase by 25% in 2 years at Simple Interest?

1. 12 ½ %
2. 12%
3. 10 ½ %
4. 10%
5. None of these

Answer: (a) 12 ½ %

Explanation:

To Find: Rate of Interest.

Solution: 

Let the sum be Rs. 100

Then, amount will be 25% extra of the sum

So, the amount = Rs. 125

Now, according to the above information we will calculate simple interest.

⇒ Simple Interest = Amount - Principal

⇒ Simple Interest = A - P

⇒ Simple Interest = 125 - 100

⇒ Simple Interest = Rs. 25

Now, after calculating simple interest we will calculate the rate of interest per annum.

Here, 

Principal = Rs. 100

Amount = Rs. 125

Simple Interest = Rs. 25

Time = 2 years

⇒ Rate of Interest = (100 x Simple Interest / Principal x Time)

⇒ Rate of Interest = (100 x SI / P x T)

⇒ Rate of Interest = (100 x 25 / 100 x 2)

⇒ Rate of Interest = 25 / 2

⇒ Rate of Interest = 12 ½ % per annum.

Therefore, the rate of interest = 12 ½ % per annum. 

Question 9: At what time would Rs. 5,000 amount to Rs. 5,800 at 8% per annum simple interest?

1. 1 year
2. 5 year
3. 4 year
4. 2 year
5. None of these

Answer: (d) 2 year.

Explanation:

To Given: Principal = Rs. 5,000

Amount = Rs. 5,800

Rate of Interest = 8% per annum

To find: Time =?

Solution: Here

Principal = Rs. 5,000

Amount = Rs. 5,800

Rate of Interest = 8% per annum.

Now, 

We will calculate Simple Interest

⇒ Simple Interest = Amount - Principal

⇒ Simple Interest = A - P

⇒ Simple Interest = 5800 - 5000

⇒ Simple Interest = Rs. 800

After calculating simple interest,

We have Principal = Rs. 5,000

Amount = Rs. 5,800

Rate of Interest = 8% per annum

Simple Interest = Rs. 800

Now, we have to calculate Time

⇒ Time = (100 x Simple Interest / Principal x Rate of Interest)

⇒ T = (100 x SI / P x R)

⇒ Time = (100 x 800 / 5000 x 8)

⇒ Time = (10 / 5)

⇒ Time = 2 years

Therefore, the time = 2 years.

Question 10: At what time would a sum double itself at 12 ½ % per annum simple interest?

1. 8 ⅓ year
2. 8 ½ year
3. 8 ¼ year
4. 8 year
5. None of these

Answer: (d) 8 year

Explanation:

To Given: Rate of simple interest is 12 ½ %

To find: In what time the principal amount will be doubled..

Solution: 

We can calculate time by one more method i.e.

Let the sum be Rs. 100

It is given in the question that amount is double of the sum

So, 

Amount be Rs. 200

⇒ Simple Interest = Amount - Principal

 ⇒ SI = A - P

⇒ Simple Interest = 200 - 100

⇒ Simple Interest = Rs. 100

Now, 

⇒Time = (100 x Simple Interest / Principal x Rate of Interest)

⇒ Time = (100 x SI / P x R)

⇒ Time = (100 x 100 / 100 x 25/2)

⇒ Time = (100 x 100 x 2 / 100 x 25)

⇒ Time = 200 / 25

⇒ Time = 8 years

⇒ Time = 8 years

Therefore, in 8 years the sum will double itself.

Question 11: At what time would Rs. 5,400 at 8% per annum yield the simple interest as Rs. 2,400 at 9% per annum in 4 year?

1. 2 year
2. 2 ½ year
3. 1 ½ year
4. 1 year
5. None of these

Answer: (a) 2 year

Explanation:

To Given: Principal = Rs. 2,400

Time = 4 year

Rate of Interest = 9% per annum

To Find: Simple Interest =?

Time =?

Solution: 

We will have to calculate Time and simple interest

First we will calculate simple interest.

Here Principal = Rs. 2,400

Time = 4 year

Rate of Interest = 9% per annum

⇒ Simple Interest = Principal x Time x Rate of Interest / 100)

⇒ SI = (P x T x R / 100) 

 ⇒ Simple Interest = (2400 x 4 x 9 / 100)

⇒ Simple Interest = 24 x 4 x 9

⇒ simple Interest = Rs. 864

After calculating we will calculate time

Here principal = Rs. 5,400

Simple Interest = Rs. 864

Rate of Interest = 8% per annum

⇒ Time = (100 x Simple Interest / Principal x Rate of Interest)

⇒ Time = (100 x 864 / 5400 x 8)

⇒ Time = (864 / 432)

⇒ Time = 2 year

 Question 12: The difference between the simple interest received from two different sources on Rs. 5,200 for 2 ½ year is Rs. 65. The difference between their rates of interest is.

1. 0.5%
2. 0.25%
3. 0.4%
4. 0.75%
5. None of these

Answer: (a) 0.5%

Explanation:

To Given: Principal = Rs. 5,200

Time = 2 ½ year

Simple Interest = Rs. 65

To Find: the difference between their rates of interest =?

Solution: Here

Principal = Rs. 5,200

Time = 2 ½ year

Simple Interest = Rs. 65

Let the rate of interest be 𝒙 % per annum 

Let the rate of interest be 𝒚 % per annum

Then, 

⇒ Simple Interest = (Principal x Time x Rate of Interest / 100) - (Principal x Time x Rate of Interest / 100)

⇒ 65 = (5200 x 5/2 x 𝒙/100) - (5200 x 5/2 x 𝒚/100)

⇒ 65 = (26 x 5𝒙) - (26 x 5𝒚)

⇒ 65 = (130𝒙) - (130𝒚)

⇒ 65 = 130 (𝒙 - 𝒚)

⇒ 65/130 = (𝒙 - 𝒚)

⇒ ½ = (𝒙 - 𝒚)

⇒ 0.5 % = (𝒙 - 𝒚)

Hence, the required difference is 0.5%

Question 13: A sum of Rs. 8,000 was lent partly at 7% and partly at 9% simple interest. If the total annual interest is Rs. 620. The ratio in which the money was lent at given rates is.

1. 5 : 3
2. 1 : 4
3. 2 : 3
4. 3 : 4
5. None of these

Answer: (a) 5 : 3

Explanation:

To given: principal = Rs. 8,000

Simple interest = Rs. 620

Rate of Interest = 7% and 9%

To Find: the ratio in which the money was lent at given rates

Solution: 

Here 

Principal amount = Rs. 8,000

Simple Interest = Rs. 620

Rate of Interest = 7% and 9%

Let the money invested at the two rates be Rs. 𝒙 and Rs. (8000 - 𝒙)

Then,

⇒ (𝒙 x 7 x 1 / 100) + (8000 - 𝒙) x 9/100 x 1 = 620

⇒ (7𝒙 / 100) + 720 - 9𝒙 / 100 = 620

⇒ 2𝒙 / 100 = 720 - 620

⇒ 2𝒙 / 100 = 100

⇒ 2𝒙 = 100 x 100

⇒ 2𝒙 = 10000

⇒ 𝒙 = 10000 / 2

⇒ 𝒙 = Rs. 5,000

Money invested is in the ratio = 𝒙 : (8000 - 𝒙)

⇒ Money invested is in the ratio = 5000 : (8000 - 5000)

⇒ Money invested is in the ratio = 5000 : 3000

⇒ Money invested is in the ratio = 5 : 3

Question 14: A man buys a music system valued at Rs. 8,000. He pays Rs. 3,500 at once and the rest 18 months later on which he is charged simple interest at the rate of 8% per annum. Find the total amount he pays for the music system.

1. Rs. 9,260
2. Rs. 8,540
3. Rs. 8,720
4. Rs. 9,410
5. None of these

Answer: (b) Rs. 8,540

Explanation:

To given: Cost of the music system = Rs. 8,000

Money paid at once = Rs. 3,500

Time = 18 months

Rate of Interest = 8 % per annum

To find: the total amount he pays for the music system.

Solution: Here

Cost of the music system = Rs. 8,000

Money paid at once = Rs. 3,500

Time = 18 months 

Rate of Interest = 8 % per annum

⇒ Time = 18 months = 18 / 12

⇒ Time = 1 ½ year

First we will calculate the money left.

Cost of the music system = Rs. 8,000

Money paid at once = Rs. 3,500

⇒ Money left = 8,000 - 3,500

⇒ Money left = Rs. 4,500

Now we will calculate simple interest,

Here Principal amount = Rs. 4,500

Time = 1 ½ year = 3 / 2 year

Rate of Interest = 8% per annum

⇒ Simple Interest = (Principal x Time x Rate / 100)

⇒ SI = (P x R x T / 100)

⇒ Simple Interest = (4500 x 3/2 x 8 / 100)

⇒ Simple Interest = (45 x 3 x 4)

⇒ Simple Interest = Rs. 540

⇒ Money to be paid at the end = 4500 + 540

⇒ Money to be paid at the end = Rs. 5,040

Cost of music system = 3500 + 5040

⇒ Cost of music system = Rs. 8,540

Therefore, the cost of the music system = Rs. 8,540

Question 15: A sum of Rs. 5,000 was lent at 6% per annum and Rs. 6,000 at 7% per annum simple interest. After what time would the total interest be Rs. 1,080?

1. 1 ¼ year
2. 1 ⅓ year
3. 1 ½ year
4. 1 ⅙ year
5. None of these

Answer: (c) 1 ½ year

Explanation:

To Given: Principal ₁ = Rs. 5,000

Principal ₂ = Rs. 6,000

Rate of interest ₁ = 6%

Rate of interest ₂ = 7%

To Find: After what time would the total interest be Rs. 1,080?

Solution: 

Here Principal ₁ = Rs. 5,000

Principal ₂ = Rs. 6,000

Rate of interest ₁ = 6%

Rate of interest ₂ = 7%

Let the time be 𝒙 year.

We will calculate simple interest by taking both the principal and rate of interest.

⇒ Simple Interest ₁ = (Principal ₁ x Time x Rate ₁ / 100)

⇒ SI₁ = (P ₁ x R ₁ x T / 100)

⇒ Simple Interest ₁ = (5000 x 𝒙 x 6 / 100)

⇒ Simple Interest ₁ = (50 x 𝒙 x 6)

⇒ Simple Interest ₁ = 300𝒙

⇒ Simple Interest ₂ = (Principal ₂ x Time x Rate ₂ / 100)

⇒ SI ₂ = (P ₂ x R ₂ x T / 100)

⇒ Simple Interest ₂ = (6000 x 𝒙 x 7 / 100)

⇒ Simple Interest ₂ = (60 x 𝒙 x 7)

⇒ Simple Interest ₂ = 420𝒙

⇒ Rate of interest = Rate of interest ₁ + Rate of interest ₂

⇒ 1080 = (300𝒙 + 420𝒙)

⇒ 1080 = 720𝒙

⇒ 1080 / 720 = 𝒙

⇒ 3/2 = 𝒙

⇒ 𝒙 = 1 ½ year