Simple Interest All Competence Aptitude

Let's denote the sum lent out at both 7% and 5% as \(x\).

The interest earned on the sum lent out at 7% for 4 years is given by \(0.07x \times 4 = 0.28x\).

Similarly, the interest earned on the sum lent out at 5% for 4 years is given by \(0.05x \times 4 = 0.20x\).

The total interest earned on both loans is the sum of these interests, which is given as 960:

\[0.28x + 0.20x = 960\]

\[0.48x = 960\]

Now, let's solve for \(x\):

\[x = \dfrac{960}{0.48}\]

\[x = 2000\]

So, the total sum lent out is \(\boxed{Rs. 2000}\).

To find the principal amount borrowed by the man, we'll use the formula for simple interest:

\[ \text{Simple Interest} = \dfrac{P \times R \times T}{100} \]

Where:
- \( P \) is the principal amount
- \( R \) is the rate of interest per annum
- \( T \) is the time in years

Given that the rate of interest is 12% per annum, and the simple interest earned after 3 years is Rs. 5400, we can set up the equation:

\[ 5400 = \dfrac{P \times 12 \times 3}{100} \]

\[ 5400 = \dfrac{36P}{100} \]

To find \( P \), we can solve this equation:

\[ P = \dfrac{5400 \times 100}{36} \]

\[ P = \dfrac{540000}{36} \]

\[ P = 15000 \]

So, the principal amount borrowed by him was \(\boxed{Rs. 15,000}\).

To find the amount to be paid, we'll use the formula for simple interest:

\[ \text{Simple Interest} = \dfrac{P \times R \times T}{100} \]

Where:
- \( P \) is the principal amount (Rs. 2000)
- \( R \) is the rate of interest per annum (5%)
- \( T \) is the time in years (2 years)

First, let's calculate the simple interest:

\[ \text{Simple Interest} = \dfrac{2000 \times 5 \times 2}{100} = \dfrac{2000 \times 10}{100} = 200 \]

Now, the amount to be paid is the sum of the principal and the simple interest:

\[ \text{Amount} = P + \text{Simple Interest} = 2000 + 200 = 2200 \]

So, the amount to be paid is \(\boxed{Rs. 2200}\).

To calculate the simple interest paid on the amount paid at the end of 2 years, we first need to find out how much Ram paid at the end of 2 years.

Ram bought the bike for Rs. 60,000 and paid Rs. 10,000 as cash down payment. So, the remaining amount paid at the end of 2 years is:

\[ 60,000 - 10,000 = Rs. 50,000 \]

Now, we'll find out the simple interest on Rs. 50,000 at the rate of 15% for 2 years using the formula:

\[ \text{Simple Interest} = \dfrac{P \times R \times T}{100} \]

Where:
- \( P \) is the principal amount (Rs. 50,000)
- \( R \) is the rate of interest per annum (15%)
- \( T \) is the time in years (2 years)

Substituting the values:

\[ \text{Simple Interest} = \dfrac{50,000 \times 15 \times 2}{100} = \dfrac{50,000 \times 30}{100} = Rs. 15,000 \]

So, Ram paid Rs. 15,000 more as simple interest. Therefore, the correct option is \(\boxed{\text{Rs. 15,000}}\).

To solve this problem, we first need to find the rate of interest per annum using the given information.

Let's denote:
- \( P \) as the principal amount (Rs. 800)
- \( A \) as the amount after 3 years (Rs. 920)
- \( T \) as the time in years (3 years)

We can use the formula for simple interest to find the rate of interest (\( R \)):\[ A = P + \text{Simple Interest} \]\[ 920 = 800 + \text{Simple Interest} \]\[ \text{Simple Interest} = 920 - 800 = 120 \]

Now, we can use the formula for simple interest to find the rate (\( R \)):\[ \text{Simple Interest} = \dfrac{P \times R \times T}{100} \]\[ 120 = \dfrac{800 \times R \times 3}{100} \]\[ 120 = \dfrac{24R}{100} \]\[ 12000 = 24R \]\[ R = \dfrac{12000}{24} = 500 \]

So, the initial rate of interest is \( R = 5\% \).

Now, if the interest rate is increased by 3%, the new rate would be \( R + 3\% = 5\% + 3\% = 8\% \).

Let's find out the amount after 3 years with the new interest rate:\[ \text{New Amount} = P + \text{New Simple Interest} \]\[ \text{New Amount} = 800 + \left( \dfrac{800 \times 8 \times 3}{100} \right) \]\[ \text{New Amount} = 800 + \left( \dfrac{19200}{100} \right) \]\[ \text{New Amount} = 800 + 192 \]\[ \text{New Amount} = Rs. 992 \]

So, if the interest rate is increased by 3%, the new amount after 3 years would be \(\boxed{Rs. 992}\).

2.1 percent 

To solve this problem, let's break it down step by step:

Let's say Alipta received an amount of money \( P \) from her father. The simple interest obtained from this amount after \( n \) years at a rate of \( 6\% \) per annum can be calculated using the formula:

\[ \text{Interest} = \dfrac{P \times n \times R}{100} \]

Where:
- \( P \) is the principal amount (the amount of money Alipta received from her father).
- \( n \) is the time in years.
- \( R \) is the rate of interest per annum.

According to the problem, after \( n \) years, the ratio of the money (\( P \)) and the interest obtained (\( \text{Interest} \)) is \( 10:3 \).

So, we can write the ratio as:

\[ \dfrac{P}{\text{Interest}} = \dfrac{10}{3} \]

Now, substitute the expressions for \( P \) and \( \text{Interest} \) and solve for \( n \):

\[ \dfrac{P}{\dfrac{P \times n \times R}{100}} = \dfrac{10}{3} \]

Solving this equation will give us the value of \( n \), which represents the number of years.

\[ \dfrac{100}{n \times R} = \dfrac{10}{3} \]

Given that the rate \( R \) is \( 6\% \) (or \( 6 \) in decimal form), substitute it into the equation:

\[ \dfrac{100}{6n} = \dfrac{10}{3} \]

Now, cross multiply:

\[ 3 \times 100 = 10 \times 6n \]

\[ 300 = 60n \]

Now, solve for \( n \):

\[ n = \dfrac{300}{60} \]

\[ n = 5 \]

So, the ratio of money to interest will be \( 10:3 \) after \( 5 \) years.

Therefore, the correct answer is: 5 years.

To find the sum of money that will give 1 as interest per day at the rate of 5% per annum simple interest, we need to use the formula for simple interest:

\[ \text{Simple Interest} = \dfrac{P \times R \times T}{100} \]

Where:
- \( P \) is the principal amount (the sum of money we want to find).
- \( R \) is the rate of interest per annum.
- \( T \) is the time in years.

Given that we want to find the principal amount such that the interest earned per day is 1, we'll set \( T = \dfrac{1}{365} \) (since there are 365 days in a year) and \( R = 5\% \).

Now, we can rearrange the formula to solve for \( P \):

\[ P = \dfrac{\text{Simple Interest} \times 100}{R \times T} \]

Substituting the given values:

\[ P = \dfrac{1 \times 100}{5 \times \dfrac{1}{365}} \]

\[ P = \dfrac{100 \times 365}{5} \]

\[ P = \dfrac{36500}{5} \]

\[ P = 7300 \]

So, the sum of money that will give 1 as interest per day at the rate of 5% per annum simple interest is 7300.

Therefore, the correct answer is: 7300.

To solve this problem, let's denote the rate of interest per annum as \( R \).

For the loan to B:
- Principal (\( P_B \)) = $5000
- Time (\( T_B \)) = 2 years

For the loan to C:
- Principal (\( P_C \)) = $3000
- Time (\( T_C \)) = 4 years

The total interest received from both loans is $2200.

Using the formula for simple interest:\[ \text{Simple Interest} = \dfrac{P \times R \times T}{100} \]

We can set up two equations based on the information given:

1. For the loan to B:\[ \text{Interest from B} = \dfrac{5000 \times R \times 2}{100} = 100R \]

2. For the loan to C:\[ \text{Interest from C} = \dfrac{3000 \times R \times 4}{100} = 120R \]

Given that the total interest received from both loans is $2200:\[ \text{Interest from B} + \text{Interest from C} = 100R + 120R = 2200 \]

\[ 220R = 2200 \]

\[ R = \dfrac{2200}{220} \]

\[ R = 10 \]

So, the rate of interest per annum is 10%.

Therefore, the correct answer is: 10%.

To find the rate of interest per annum, let's denote it as \( R \).

For the loan to B:
- Principal (\( P_B \)) = $6000
- Time (\( T_B \)) = 2 years

For the loan to C:
- Principal (\( P_C \)) = $1500
- Time (\( T_C \)) = 4 years

The total interest received from both loans is $900.

Using the formula for simple interest:\[ \text{Simple Interest} = \dfrac{P \times R \times T}{100} \]

We can set up two equations based on the information given:

1. For the loan to B:\[ \text{Interest from B} = \dfrac{6000 \times R \times 2}{100} = 120R \]

2. For the loan to C:\[ \text{Interest from C} = \dfrac{1500 \times R \times 4}{100} = 60R \]

Given that the total interest received from both loans is $900:\[ \text{Interest from B} + \text{Interest from C} = 120R + 60R = 900 \]

\[ 180R = 900 \]

\[ R = \dfrac{900}{180} \]

\[ R = 5 \]

So, the rate of interest per annum is 5%.

Therefore, the correct answer is: 5%.