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

Given:

A certain sum becomes 3 times itself in 6 years at simple interest.

Principal (P) = ₹X

Amount after 6 years (A) = ₹3X

Time for 3X = 6 years

Amount after unknown time (t) = ₹9X

Formula used:

Simple Interest (SI) = P × r × t / 100

Total Amount (A) = P + SI

Calculation:

For 3X:

SI = A - P

⇒ ₹3X - ₹X = ₹2X

SI = ₹2X

Using SI formula:

₹2X = ₹X × r × 6 / 100

⇒ r = (2 × 100) / 6

⇒ r = 33.33%

For 9X:

SI = ₹9X - ₹X

⇒ SI = ₹8X

Using SI formula:

₹8X = ₹X × r × t / 100

⇒ t = (8 × 100) / 33.33

⇒ t ≈ 24 years

∴ The correct answer is option (4).

Given:

Principal (P) = ₹2400

Rate (R) = 20% per annum

Interest (I) = ₹1440

Formula used:

Simple Interest (I) = P × R × T / 100

Calculations:

1440 = 2400 × 20 × T / 100

⇒ 1440 = 480 × T

⇒ T = 1440 / 480

⇒ T = 3 years

∴ 2T = 2 × 3 = 6

Calculation

Let, sum invest in scheme A and scheme B is 4x and 3x respectively.

Compound Interest in scheme A is 4x × [44/100].  

Simple interest in scheme B is 3x × [[r + 10]/100] × 3

ATQ,

[4x × [44/100] : [3x × [[ r + 10) /100] × 3] = 22/27

Or, 176 / [r + 10] = 22 / 3

Or, 22r + 220 = 528

Or, r = [308 / 22] = 14

So, LCM of 14 and 28 is 28. 

Given:

Principal (P) = ₹1200

Amount (A) = ₹1440

Time (t) = 2 years

Formula Used:

Simple Interest (SI) = A - P

SI = \(\dfrac{P \times r \times t}{100}\)

Where, r = rate of interest

Calculations:

SI = \(\dfrac{P \times r \times t}{100}\):

240 = \(\dfrac{1200 \times r \times 2}{100}\)

⇒ 240 = 12 × r × 2

⇒ 240 = 24 × r

⇒ r = \(\dfrac{240}{24}\)

⇒ r = 10%

∴ The rate of interest is 10% per annum.

Given:

Simple Interest (SI) = ₹420

Annual Rate of Interest (R) = 10%

Time (T) = 2 years

Formula Used:

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

To find the Principal (P), rearrange the formula: P = (SI × 100) / (R × T)

Calculation:

P = (420 × 100) / (10 × 2)

P = 42000 / 20

P = 2100

∴ The principal amount is ₹2100.

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