Simple Interest — Multiple Choice Questions

Sangeeta deposited ₹ 1,000 in a bank paying interest at the rate of 10% per year. The amount in 2 years is:

1. ₹ 200

2. ₹ 800

3. ₹ 1,200

4. ₹ 1,100

Answer

P = ₹ 1,000, R = 10% and T = 2 years.

I = $\dfrac{1000 \times 10 \times 2}{100}$ = ₹ 200.

Amount = P + I = 1,000 + 200 = ₹ 1,200.

Hence, option 3 is the correct option.

Mercy invested ₹ 2,000 at 12% per year and an equal sum at 10% per year. Thus, total income from interest in one year is:

1. ₹ 440

2. ₹ 40

3. ₹ 240

4. ₹ 200

Answer

Interest on ₹ 2,000 at 12% for 1 year = $\dfrac{2000 \times 12 \times 1}{100}$ = ₹ 240.

Interest on ₹ 2,000 at 10% for 1 year = $\dfrac{2000 \times 10 \times 1}{100}$ = ₹ 200.

Total income from interest = 240 + 200 = ₹ 440.

Hence, option 1 is the correct option.

Mercy invested ₹ 5,000 at 12% per year and an equal sum at 10% per year. The difference of incomes from two investments in 2 years is:

1. ₹ 1,200

2. ₹ 1,000

3. ₹ 200

4. ₹ 2,200

Answer

Interest on ₹ 5,000 at 12% for 2 years = $\dfrac{5000 \times 12 \times 2}{100}$ = ₹ 1,200.

Interest on ₹ 5,000 at 10% for 2 years = $\dfrac{5000 \times 10 \times 2}{100}$ = ₹ 1,000.

Difference of incomes = 1,200 − 1,000 = ₹ 200.

Hence, option 3 is the correct option.

A sum of money invested for 10 years earns interest equal to the sum itself. The rate of interest is:

1. 5%

2. 10%

3. 20%

4. none of these

Answer

Let the sum be ₹ P and T = 10 years.

I = the sum itself = ₹ P.

R = $\dfrac{\text{I} \times 100}{\text{P} \times \text{T}}$%

$= \dfrac{\text{P} \times 100}{\text{P} \times 10}$%

= 10%.

Hence, option 2 is the correct option.

A sum of money invested at 5% per year, earns interest equal to half of the sum invested. The time for which the sum is invested, is:

1. 5 years

2. 10 years

3. 15 years

4. 20 years

Answer

Let the sum be ₹ P and R = 5%.

I = half of the sum = ₹ $\dfrac{\text{P}}{2}$.

$\text{ T } = \dfrac{\text{I} \times 100}{\text{P} \times \text{R}}\\[1em] = \dfrac{\dfrac{\text{P}}{2} \times 100}{\text{P} \times 5}\\[1em] = \dfrac{100}{2 \times 5}\\[1em] = 10 \text{ years }$

Hence, option 2 is the correct option.

A sum of money invested at 10% per annum, earns interest which is 1.2 times the sum invested. The time, for which the sum is invested, is:

1. 8 years

2. 10 years

3. 12 years

4. 20 years

Answer

Let the sum be ₹ P and R = 10%.

I = 1.2 times the sum = ₹ 1.2P.

$\text{ T }= \dfrac{\text{I} \times 100}{\text{P} \times \text{R}}\\[1em] = \dfrac{1.2\text{P} \times 100}{\text{P} \times 10}\\[1em] = \dfrac{120}{10}\\[1em] = 12\text{ years}$

Hence, option 3 is the correct option.

A sum of money invested at 10% per annum becomes 1.2 times the sum invested. The time, for which the sum is invested, is:

1. 2 years

2. 4 years

3. 6 years

4. 8 years

Answer

Let the sum be ₹ P and R = 10%.

Amount = 1.2 times the sum = ₹ 1.2P.

I = Amount − P = 1.2P − P = ₹ 0.2P.

$\text{ T }= \dfrac{\text{I} \times 100}{\text{P} \times \text{R}}\\[1em] = \dfrac{0.2\text{P} \times 100}{\text{P} \times 10}\\[1em] = \dfrac{20}{10}\\[1em] = 2\text{ years}$

Hence, option 1 is the correct option.

In 8 years, a sum earns interest equal to the sum invested. The rate of interest is:

1. 7.5%

2. 8%

3. 10%

4. 12.5%

Answer

Let the sum be ₹ P and T = 8 years.

I = the sum invested = ₹ P.

R = $\dfrac{\text{I} \times 100}{\text{P} \times \text{T}}$%

$= \dfrac{\text{P} \times 100}{\text{P} \times 8}$%

$= \dfrac{100}{8}$%

= 12.5%

Hence, option 4 is the correct option.

A sum of money invested at 10% per annum becomes ₹ 3,000 in 5 years. The sum invested is:

1. ₹ 1,000

2. ₹ 1,500

3. ₹ 2,000

4. ₹ 4,000

Answer

Let the sum be ₹ P, R = 10% and T = 5 years.

I = $\dfrac{\text{P} \times 10 \times 5}{100} = \dfrac{\text{P}}{2}$.

Amount = P + I

$\Rightarrow 3000 = \text{P} + \dfrac{\text{P}}{2}\\[1em] \Rightarrow 3000 = \dfrac{3\text{P}}{2}\\[1em] \Rightarrow \text{P} = \dfrac{3000 \times 2}{3} = ₹\ 2,000$

Hence, option 3 is the correct option.

₹ 4,000 becomes ₹ 5,000 in 5 years. The rate of interest is:

1. 5%

2. 10%

3. 12%

4. none of these

Answer

P = ₹ 4,000, Amount = ₹ 5,000 and T = 5 years.

I = Amount − P = 5,000 − 4,000 = ₹ 1,000.

R = $\dfrac{\text{I} \times 100}{\text{P} \times \text{T}}$%

$= \dfrac{1000 \times 100}{4000 \times 5}$%

$= \dfrac{100000}{20000}$%

$= \dfrac{10}{2}$%

= 5%.

Hence, option 1 is the correct option.