Some amount of money becomes five times is a fixed time at the rate of 6% annual simple interest. How many times it will become in the same time at the rate of 9% interest ?

Correct option is B

Given:

1. The amount becomes 5 times the principal n = 5 at a rate of R₁ = 6% in time T

2. The rate of interest is increased to R₂ = 9%, and we need to determine how many times n the principal will become in the same time T.

Formula Used:

$$A = P + \frac{P \cdot R \cdot T}{100}$$​

​$$n = 1 + \frac{R \cdot T}{100}$$

Solution:

Finding T for R₁ = 6%

From the given information, the amount becomes 5 times the principal at a rate of 6% in time T. We know that n = 5, and R₁ = 6%. Substituting these values into the formula:

​$$5 = 1 + \frac{6 \cdot T}{100}$$​​

​$$\frac{6 \cdot T}{100} = 4$$​​

$$T = \frac{4 \cdot 100}{6} = 66.67 \, \text{years}$$​

Now, we calculate how many times the principal will become in the same time at a rate of 9% using the formula:

​$$n = 1 + \frac{R_2 \cdot T}{100}$$​​

Substituting R₂ = 9%and T = 66.67 years

​$$n = 1 + \frac{9 \cdot 66.67}{100}$$​​

​$$n = 1 + \frac{600.03}{100}$$​​

$$n = 1 + 6.0003 = 7.0003$$​

At the rate of 9% interest, the amount will become approximately 7 times the principal in the same time.