Simple Interest — Assertion Reason Type Questions

Assertion (A): A sum of money doubles itself at 5% p.a. in 20 years.

Reason (R): Time = $\dfrac{100 \times \text{Interest}}{\text{Principal} \times \text{Rate}}$

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

When a sum doubles itself, I = Principal. Taking the sum as ₹ P and R = 5%,

Time = $\dfrac{100 \times \text{P}}{\text{P} \times 5} = \dfrac{100}{5}$ = 20 years.

So, Assertion (A) is true.

Time = $\dfrac{100 \times \text{Interest}}{\text{Principal} \times \text{Rate}}$ is the correct formula.

So, Reason (R) is true.

Hence, option 3 is the correct option.

Assertion (A): ₹ 250 doubles itself in 5 years at simple interest then rate of interest is 20% per month.

Reason (R): Rate % = $\dfrac{100 \times \text{Interest}}{\text{Principal} \times \text{Time}}$%.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

When ₹ 250 doubles itself, I = ₹ 250 and T = 5 years.

Rate = $\dfrac{100 \times 250}{250 \times 5} = \dfrac{100}{5}$ = 20% per annum (per year), not 20% per month.

So, Assertion (A) is false.

Rate % = $\dfrac{100 \times \text{Interest}}{\text{Principal} \times \text{Time}}$% is the correct formula.

So, Reason (R) is true.

Hence, option 2 is the correct option.

Assertion (A): The simple interest on ₹ 850 from 10^th March to 2^nd August at 2% p.a. is ₹ 6.80.

Reason (R): Amount is the sum of the Principal and interest on it.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

The starting date (10^th March) is not included and the last date (2^nd August) is included.

Time = (31 − 10) + 30 + 31 + 30 + 31 + 2

= 21 + 30 + 31 + 30 + 31 + 2

= 145 days = $\dfrac{145}{365}$ years.

$\text{ I } = \dfrac{\text{P} \times \text{R} \times \text{T}}{100} \\[1em] = \dfrac{850 \times 2 \times \dfrac{145}{365}}{100} \\[1em] = \dfrac{850 \times 2 \times 145}{100 \times 365}\\[1em] = \dfrac{246500}{36500} \\[1em] \approx ₹ 6.75$

So, Assertion (A) is false.

Amount = Principal + Interest, which is correct.

So, Reason (R) is true.

Hence, option 2 is the correct option.