Simple Interest MCQ Quiz - Objective Question with Answer for Simple Interest - Download Free PDF

Given:

Rate of interest (r) = 8%

Time (t) = 10 years

Simple Interest (SI) = ₹17,600

Formula used:

SI = P × r × t / 100

Calculations:

17600 = P × 8 × 10 / 100

⇒ 17600 = P × 80 / 100

⇒ 17600 = P × 0.8

⇒ P = 17600 / 0.8

⇒ P = ₹22,000

∴ The principal is ₹22,000.

Given:-

Principle is P, Q

Time:- 3, 4 (years) 

Formula Used:-

Simple Interest = (P × R × T)/100

Calculation:-

Simple interest on P = (P × 5 × 3)/100

Simple interest on Q = (Q × 7 × 4)/100

⇒ 15P/100 = 3 × (28Q)/100

P/Q= 28/5

P = 5.6Q

Hence the answer is P = 5.6Q.

Given:

Amount = Rs. 4,900

Rate of interest = 7.5% p.a simple interest

Time = 3 years 4 months = 10/3 years

Formula used:

SI = \(\frac{P × R × T}{100}\)

Amount = Principal + SI

Calculation:

Let the sum be 100x

SI = \(\frac{100x × 7.5 × 10}{100 × 3}\) = 75x/3

SI = 25x

∴ Amount = 100x + 25x = 125x

⇒ 125x = 4900

⇒ 5x = 196

⇒ 100x = 3920

∴ The sum = Rs. 3920

Now SI on Rs. 3920 at the rate of 8% and for the time 15/4 years

⇒ SI = \(\frac{3920 × 8 × 15}{100 × 4}\) = 392 × 3 = 1176

The amount = 3920 + 1176 = 5096

∴ The required amount is Rs. 5096.

Shortcut Trick Using, total rate of SI = Rate × Time

SI₁ = 7.5 × (10/3) = 25%

A₁ = 125%

And, SI₂ = 8 × (15/4) = 30%

A₂ = 130%

As, A₁ = 4900

⇒ 125% → 4900

⇒ 130% → 5096

⇒ A₂ = Rs. 5096

∴∴ The required amount is Rs. 5096. 

Given:

Total investment = Rs. 15,500 

The annual rates of simple interest for these schemes are 4%, 6%, and 10% respectively.

At the end of one year, the interest earned from all three schemes is the same.

Concept Used:

Simple Interest, I = PRT/100,

where P is the principal (the initial amount of money),

R is the rate of interest, and

T is the time in years.

Calculation:

Let's denote the sums invested in the schemes with rates 4%, 6%, and 10% as P1, P2, and P3 respectively.

We know that P1 + P2 + P3 = Rs. 15,500.

We are also given that the interests earned from these investments after one year are the same, which gives us two more equations:

I1 = I2 and I1 = I3,

Substituting I = PRT/100 into these equations gives:

P1 ×  4/100 = P2 × 6/100, and

P1 × 4/100 = P3 × 10/100.

From the first equation, we find P2 = P1 × 2/3.

From the second equation, we find P3 = P1 × 2/5.

Substituting these expressions for P2 and P3 into the equation P1 + P2 + P3 = 15,500, we get:

P1 + P1 × 2/3 + P1 × 2/5 = 15,500,

Solving this equation for P1 gives:

P1 = 15,500 / (1 + 2/3 + 2/5)

⇒ 15,500 / (15/15 + 10/15 + 6/15)

⇒ 15,500 / 31/15 = Rs. 7,500.

So, the sum invested at the rate of 6% (P2) is:

⇒ P2 = P1 × 2/3

⇒ 7,500 × 2/3 = Rs. 5,000.

∴ Option 2 is the correct answer.

Given:

Principal amount (P) = Rs. 9,000

Time (T) = 7 years

Ratio between total interest and principal = 7 : 10

Formula used:

Simple Interest (SI) = (P × R × T) / 100

Calculation:

We are given that the ratio of the total interest (SI) to the principal amount (P) is 7 : 10. This means:

SI / P = 7 / 10

Substitute P = 9000 into the equation:

SI / 9000 = 7 / 10

SI = (7 / 10) × 9000

SI = 6300

∴ The simple interest is Rs. 6300.

Given: 

Amount produce in 7 years = Rs.14522

Amount produce in 11 years = Rs.18906

Formula used:

Simple interest (S.I) = (P × R × T)/100

Calculation:

Amount produce in 7 years = Rs.14522

Amount produce in 11 years = Rs.18906

S.I produced in (11 - 7) = 4 years = (18906 - 14522) = Rs.4384

S.I in 1 years = 4384/4 = 1096

Principal = 14522 - (1096 × 7)

⇒ (14522 - 7672) = Rs.6850

∴ The correct answer is Rs.6850.

Concept Used:

In this type of question, number can be calculated by using the below formulae

Formula Used:

If a sum with simple interest rate, amounts to Rs. ‘A’ in y years. and Rs. ‘B’ in z years. then,

P = (A × z – B × y)/(z – y)

Calculation:

Using the above formulae, we have

⇒ P = (10650 × 6 – 11076 × 5)

⇒ P = Rs. 8520

∴ Required principal is Rs. 8520 

A sum becomes Rs. 10650 in 5 years. and Rs. 11076 in 6 years. at simple interest

Interest of 1 year = 11076 – 10650 = Rs. 426

Interest of 5 year = 426 × 5 = 2130

∴ Required principal = 10650 – 2130 = Rs. 8520

Given:

Principal = Rs. 8000

Rate = 10%

Time =  \(2\frac{2}{5}\) years

Formula used:

SI = (P × t × r)/100

CI = P(1 + r/100)^t - P

P = Principal

t = time

r = rate

Calculation:

SI = (8000 × 12 × 10)/(100 × 5)

⇒ Rs. 1920

CI = 8000[1 + 10/100]² × [1 + 4/100] - 8000

⇒ 8000 × 11/10 × 11/10 × 26/25 - 8000

⇒ 10067.2 - 8000

⇒ 2067.2

Difference = 2067.2 - 1920 = 147.2

∴ Required difference is Rs. 147.2

Shortcut Trick 

So, the difference of CI and SI = 80 + 32 + 32 + 3.2

∴ The Difference of CI and SI = 147.2.

Given:

Amount = 2P

Time = 10 years

Formula used:

SI = (PRT/100) 

Amount = (PRT/100) + P

Calculation:

Amount = (PRT/100) + P

2P = (PR/10) + P 

⇒ P = (PR/10) 

⇒ R = 10%

According to the question, Amount = 3P

3P = (10PT/100) + P 

⇒ 2P = (PT/10)

⇒ T = 20 years

 ∴ Time taken to triple the amount is 20 years.

Shortcut TrickInterest = 2P - P = P = 100% of principle

Time = 10 year

Hence, rate = Interest/Time = 100/10 = 10%

New interest = 3P - P = 2P = 200% of principle

∴ Time = Interest/Rate = 200/10 = 20 Years

Interest earned for 5 years – Interest earned for 4 years = 375

Let the principal be Rs. P,

⇒ (P × 7.5 × 5) /100 – (P × 7.5 × 4) /100 = 375

⇒ (37.5 × P) /100 – (30 × P) /100 = 375

⇒ (7.5 × P) /100 = 375

Given:

Amount after 3 years = Rs. 715

Amount after 8 years  = Rs. 990

Formula used:

A = P + SI

Where A = amount , P = Principle

And SI = Simple interest

Calculation:

Amount in 3 years = Rs. 715

Now it is given in the question, amount for the time of further 5 years i.e 

Total time = 5 years + 3 years = 8 years.

Amount in 8 years = Rs. 990

SI for 5 years = Amount after 8 years  - Amount after 3 years

⇒ SI for 5 years = 990 - 715 = 275

SI for 1 years = 275/5 = 55

SI for 3 years = 55 × 3 = Rs.165

P = Amount of 3 years - SI of 3 years

⇒ P = 715 - 165 = 550

∴  The sum is Rs. 550

Confusion Points It is given in the question that after further 5 years amount is calculated , so total time will be (5 +3) years = 8 years. not 5 years.

Let P = principal, R = rate of interest and N = time period

Simple interest = PNR/100

Given,

N = 5 years​

Then,

⇒ 2/5 × P = (P × R × 5)/100

⇒ R = 200/25

\(\therefore {\rm{\;}}R = 8 % \) %

Given:

The simple interest for 6 years on a sum = 29250

Formula used:

\(SI\ =\ {P\ \times R\ \times T \over 100}\)     (Where SI = Simple interest, P = Principle, R = The rate, and T = The time)

Calculation:

Let us assume the sum be P

⇒ The simple interest for the first 2 years at a 7% rate = \(\ {P\ \times 7\ \times 2 \over 100}\ = {14P\over 100}\)

⇒ The simple interest for the next 4 years at a 16% rate = \(\ {P\ \times 16\ \times 4 \over 100}\ = {64P\over 100}\) 

⇒ The total simple interest = 29250

⇒ \({14P\over 100}\ +\ {64P\over 100}\ =\ 29250\)

\({78P\over 100}\ =\ 29250\)

⇒ By solving 

⇒ The required sum = P = 37500

∴ The required result will be 37500.

Given:

Principle = Rs. 2700

Time = 8 months = 8/12 year = 2/3 year

Rate of interest = 5 paisa per month = 5 × 12 paisa per year = 60 paisa per year = 60 %

Formula used:

SI = PRT/100

Calculation:

SI = (2700 × 60 × 2) / (100 × 3)

⇒ 9 × 120

⇒ 1080

∴ The SI will be Rs. 1080.

Given:

Principle, P = Rs. 32,000

Rate, r = 8.5%

Time, t = (18 + 31 + 24) / 365 = 73 / 365 = 1 / 5 years

Concept used:

Simple Interest = (P × r × t) / 100

Calculation:

SI = (32,000 × 8.5 × 1 / 5) / 100

⇒ (32 × 85) / 5

⇒ 32 × 17