Simple Interest — Statement I-II Type Questions

Statement 1: ₹ 400 will yield an interest of ₹ 36 in 3 years at 3% p.a.

Statement 2: Rate percent is the interest paid on ₹ 100 for any period of time.

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Solving,

$\text{ I }= \dfrac{\text{P} \times \text{R} \times \text{T}}{100}\\[1em] = \dfrac{400 \times 3 \times 3}{100}\\[1em] = \dfrac{3600}{100}\\[1em] = ₹\ 36$

So, Statement 1 is true.

Rate percent (per annum) is the interest on ₹ 100 for a specific period of time, not for any period of time.

So, Statement 2 is false.

Hence, option 3 is the correct option.

Statement 1: If both rate percent and time are equal, then simple interest on a certain sum is $\dfrac{16}{25}$ times of the sum.

Statement 2: The value of interest depends on (i) Sum, (ii) Rate of interest p.a. and (iii) time in years.

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Let the sum be ₹ P and rate = time = n.

Then I = $\dfrac{\text{P} \times n \times n}{100} = \dfrac{n^2\text{P}}{100}$.

This equals $\dfrac{16}{25}$ times the sum only when $\dfrac{n^2 \text {P}}{100} = \dfrac{16 \text{P}}{25}$, i.e. n = 8. For any other equal values of rate and time (say n = 5), the interest is not $\dfrac{16}{25}$ of the sum.

So, Statement 1 is false.

Since I = $\dfrac{\text{P} \times \text{R} \times \text{T}}{100}$, the interest depends on the Sum, the Rate of interest p.a. and the time in years.

So, Statement 2 is true.

Hence, option 4 is the correct option.