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 this regard?
Question
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 this regard?
Solution
To determine which statement is true, let's break down the information given:
A lends a sum of money for 10 years at 5% simple interest (SI). B lends double the amount for 5 years at the same rate of interest.
First, let's calculate the interest earned by A over 10 years. The formula for simple interest is:
Interest = Principal * Rate * Time
Since A lends a sum of money for 10 years at 5% SI, the interest earned by A can be calculated as:
Interest_A = Principal_A * Rate_A * Time_A = Principal_A * 0.05 * 10
Now, let's calculate the interest earned by B over 5 years. Since B lends double the amount, the principal for B can be calculated as:
Principal_B = 2 * Principal_A
Using the same formula for simple interest, the interest earned by B can be calculated as:
Interest_B = Principal_B * Rate_B * Time_B = (2 * Principal_A) * 0.05 * 5
Now, let's compare the two statements:
Statement 1: The interest earned by A is greater than the interest earned by B. Statement 2: The interest earned by B is greater than the interest earned by A.
To determine which statement is true, we need to compare the values of Interest_A and Interest_B. If Interest_A is greater than Interest_B, then Statement 1 is true. If Interest_B is greater than Interest_A, then Statement 2 is true.
By comparing the formulas for Interest_A and Interest_B, we can see that Interest_B is greater than Interest_A because Principal_B is twice the value of Principal_A. Therefore, Statement 2 is true in this regard.
In conclusion, the correct statement is: "The interest earned by B is greater than the interest earned by A."
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