A lends a sum of money for 10 years at 5% SI. B lends double the amount for 5 years at the same rate of interest . Which of the following statements is true in his regard ?

Options

A. A will get twice the amount of interest that B would get
B. B will get twice the amount of interest that A would get
C. A will get same the amount of interest that B would get
D. B will get four time the amount of interest that A would get

Answer

To solve the problem, we need to calculate the simple interest earned by both A and B and compare the results.

### Step 1: Define the variables
Let the principal amount lent by A be \( P = x \).

### Step 2: Calculate A's Simple Interest
A lends the amount for 10 years at a rate of 5%. The formula for simple interest (SI) is:

\[ SI = \frac{P \times r \times t}{100} \]

For A:
- Principal \( P = x \)
- Rate \( r = 5\% \)
- Time \( t = 10 \) years

Substituting the values into the formula:

\[ SI_A = \frac{x \times 5 \times 10}{100} = \frac{50x}{100} = \frac{x}{2} \]

### Step 3: Calculate B's Simple Interest
B lends double the amount of A, so the principal amount for B is \( P = 2x \). B lends this amount for 5 years at the same rate of 5%.

For B:
- Principal \( P = 2x \)
- Rate \( r = 5\% \)
- Time \( t = 5 \) years

Substituting the values into the formula:

\[ SI_B = \frac{2x \times 5 \times 5}{100} = \frac{50x}{100} = \frac{x}{2} \]

### Step 4: Compare the Simple Interests
Now we compare the simple interests earned by A and B:

- Simple Interest for A: \( SI_A = \frac{x}{2} \)
- Simple Interest for B: \( SI_B = \frac{x}{2} \)

### Conclusion
Since both A and B have the same simple interest, the correct statement is:

**A will get the same amount of interest that B would get.**