[Solved] Simple and Compound Both MCQ [Free PDF] - Objective Question Answer for Simple and Compound Both Quiz - Download Now! (2024)

1. ₹16,000
2. ₹12,000
3. ₹10,000
4. ₹8,000

The Correct answer is Option 2.

Key Points

Let the total principal amount be P

Compound interest for two years on 2/3P at 10%:

CI = 0.14P

Simple interest for two years on 1/3P at 15%:

SI = 0.10P

Step 3: Difference between Compound Interest and Simple Interest
The difference between compound interest and simple interest is ₹480:

0.14P - 0.10P = 480

0.04P = 480

P = 480}/{0.04} = 12,000

The total principal amount is ₹12,000. Hence, Option 2 is correct.

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1. ₹6600
2. ₹6700
3. ₹5600
4. ₹4600
5. ₹5100

Given:

Time period = 2 years

Compound Interest (CI) rate = 20% per annum

Simple Interest (SI) rate = 30% per annum

Difference between CI and SI after 2 years = ₹896

Formula used:

CI = P\((1+\frac{r}{100})^t - P\)

SI = P × \(\frac{r \times t}{100}\)

Difference = CI - SI

Calculation:

Calculation:

Let the principal amount be ₹P.

CI for 2 years:

CI = P\((1+\frac{20}{100})^2 - P\)

⇒ CI = P\((\frac{120}{100})^2 - P\)

⇒ CI = P\(\frac{144}{100} - P\)

⇒ CI = 1.44P - P = 0.44P

⇒ CI = 44% of ₹P

SI for 2 years:

SI = P × \(\frac{30 \times 2}{100}\)

⇒ SI = P × 0.60

⇒ SI = 60% of ₹P

Given Difference = ₹896

⇒ SI - CI = 60% of ₹P - 44% of ₹P

⇒ 16% of ₹P = ₹896

⇒ 0.16P = ₹896

⇒ P = ₹896 / 0.16

⇒ P = ₹5600

∴ The invested amount or principal is ₹5600.

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1. Rs. 5480
2. Rs. 4320
3. Rs. 4850
4. Rs. 5220

Given:

Principal (P) = ₹18,000

Compound Interest (CI) = ₹2,995.2

Time (t) = 2 years

Formula used:

Compound Interest formula: CI = P × ((1 + r/100)^t - 1)

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

Calculations:

2995.2 = 18000 × ((1 + r/100)² - 1)

⇒ 2995.2 / 18000 = (1 + r/100)² - 1

⇒ 0.1664 = (1 + r/100)² - 1

⇒ (1 + r/100)² = 1 + 0.1664 = 1.1664

⇒ 1 + r/100 = √1.1664 = 1.08

⇒ r/100 = 1.08 - 1 = 0.08

⇒ r = 8%

Now, calculate Simple Interest for 3 years:

SI = (18000 × 8 × 3) / 100 = 4320

∴ The Simple Interest accrued is ₹4,320.

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1. Rs. 1080
2. Rs. 2100
3. Rs. 2160
4. None of the above

Given:

Compound interest (CI) = Rs. 1270

Rate (R) = 16²/3% per annum

Time (T) = 3 years

Formula Used:

CI = P(1 + R/100)^T - P

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

Calculation:

Let the principal amount be P.

CI = P(1 + 50/3 × 1/100)³ - P

⇒ 1270 = P(1 + 1/6)³ - P

⇒ 1270 = P(7/6)³ - P

⇒ 1270 = P(343/216 - 1)

⇒ 1270 = P(127/216)

⇒ P = 1270 × 216 / 127

⇒ P = 2160

Now, calculate Simple Interest:

SI = P × R × T / 100

⇒ SI = 2160 × 50/3 × 1/100 × 3

⇒ SI = 2160 × 1/2

⇒ SI = 1080

The simple interest per annum on the same sum at the same rate and for the same period is Rs. 1080.

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1. Rs. 60.5
2. Rs. 62.5
3. Rs. 80.62
4. Rs. 70.62

Given:

Principal (P) = ₹25,000

Rate (r) = 5% per annum

Time (t) = 2 years

Formula used:

Simple Interest (SI) =\(\dfrac{P × r × t}{100}\)

Compound Interest (CI) =\(P (1+\dfrac{r}{100})^t - P\)

Calculation:

SI =\(\dfrac{25000 × 5 × 2}{100}\)

⇒ SI = ₹2,500

CI =\(25000 (1+\dfrac{5}{100})^2 - 25000\)

⇒ CI =\(25000 (1.05)^2 - 25000\)

⇒ CI = ₹27,562.5 - ₹25,000

⇒ CI = ₹2,562.5

Difference = CI - SI

⇒ Difference = ₹2,562.5 - ₹2,500

⇒ Difference = ₹62.5

∴ The correct answer is option (2).

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Simple and Compound Both Question 6

1. 9%
2. 8%
3. 11%
4. 10%

Simple and Compound Both Question 6 Detailed Solution

Given:

C.I for 2 years = Rs. 304.5

S.I for 2 years = Rs. 290

Calculation:

S.I for 1 year = Rs. (290/2) = Rs. 145

Difference between S.I and C.I = Rs. (304.5 – 290)

⇒ Rs. 14.5

Rate of interest per annum = (14.5/145) × 100%

⇒ 10%

∴ The rate of interest per annum is 10%

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Simple and Compound Both Question 7

1. ₹ 280000
2. ₹ 85000
3. ₹ 80000
4. ₹ 75000

Simple and Compound Both Question 7 Detailed Solution

Given:

The difference between the simple interest and compound interest (interest is compounded half yearly) on a sum at the rate of 25% per annum for one year is ₹ 4375

Formula used:

Simple Interest = (P×N× R)/100

Compound Interest = [P(1 + (r/200))^T]- P (for compounded half yearly)

Calculation:

Let P be the Principal,

S.I = (P× 1× 25)/100 = P/4

C.I = [P(1 + (25/200))²] - P (T = 2 ∵ compounded half yearly for 1 year)

⇒ C.I = 17P/64

Now, C.I - S.I = (17P/64) - (P/4) = P/64

⇒ P/64 = 4375

∴ P = 64× 4375 = 280000

Shortcut TrickFormula used:

CI - SI = P(R/100)²

Rate (R) = 25%/2 due to the compounded half-yearly.

⇒ 4375 = P (25/200)²

⇒ P = 4375× 64

⇒ P = 280,000

∴ The sum is Rs. 280,000.

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Simple and Compound Both Question 8

1. ₹ 93750 and 4%
2. ₹ 93750 and 5%
3. ₹ 92500 and 6%
4. ₹ 92500 and 7%

Simple and Compound Both Question 8 Detailed Solution

Given data:

SI for 3 years = Rs 11,250

CI for 2 years at the same rate = Rs 7650

Formula used:

P =\(SI\times 100\over {R\times T}\)where-

P = Principal

SI = Simple Interest

R = Rate

T = Time

Calculation:

SI for 1 year = 11,250 ÷ 3 = Rs 3,750

SI for 2 year = 2 × 3750 = Rs 7500

Difference between CIand SI for 2 year = 7650 - 7500 = Rs 150

⇒ This difference between CIand SI was on the SI for the 1st year i.e., Rs 3750

∴Rate % =\(150\over 3750\)× 100 = 4%

Principal =\(3750\times 100\over {1\times4}\)= Rs 93,750

∴ The Principal amount was Rs 93,750 and the rate of interest was 4%.

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Simple and Compound Both Question 9

1. Rs. 500
2. Rs. 450
3. Rs. 650
4. Rs. 550

Simple and Compound Both Question 9 Detailed Solution

Calculation:

The effective rate of 20% for 2years is = 20 + 20 + (20 × 20)/100 = 44%

So, C.I on 1000 for 2 years is = 1000× 44/100 = 440

Let the principal invest in S.I be P

Now, according to the question,

(P× 4× 10)/100 = 440/2

⇒ P = 1100/2 = 550

∴The principal amount be 550

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Simple and Compound Both Question 10

1. Rs. 525
2. Rs. 500
3. Rs. 200
4. Rs. 210

Simple and Compound Both Question 10 Detailed Solution

Given:

Time = 2 years, Simple Interest = 500, rate = 10%

Formula used:

Simple Interest = (Principal × Rate × Time)/100

Compound Interest = Principal[(1 + rate/100)^t – 1]

Calculation:

Let the principal be ‘P’.

Simple Interest = (Principal × Rate × Time)/100

⇒ 500 = (Principal × 10 × 2)/100

⇒ Principal = 2500

Compound Interest = Principal[(1 + rate/100)^t – 1]

⇒ 2500[(1 + 10/100)² – 1]

⇒ 525

∴ The compound Interest is Rs 525.

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Simple and Compound Both Question 11

1. 10,580
2. 10,648
3. 11,239
4. 10,450

Simple and Compound Both Question 11 Detailed Solution

Given:

The simple interest on a sum of Rs. 8,000 at a certain rate percent per annum for 3 years is Rs. 3,600.

Concept used:

Simple Interest, SI = (P× R× T)÷ 100

where

P = Principal amount

R = Rate of interest per year

T = time inyears

Compound interest, CI = P(1 + R/100)n- P

where

P = Principal amount

R = Rate of interest per year

N = time inyears

Calculation:

Let the rate of interest be R%.

According to the question,

(8000× R× 3)÷ 100 = 3600

⇒ R = 15%

Now, the same interest rate would be forcompounded 8-monthly = 15× 8/12 = 10%

So, the amount would become

⇒ 8000× (1 + 10/100)^24/8

⇒10648

∴ Rs. 10648will be the amount (in Rs.) of the same sum after 2 years at the same rate if the interest is compounded 8 months.

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Simple and Compound Both Question 12

1. Rs. 87.70
2. Rs. 87.50
3. Rs. 85.70
4. Rs. 88.70

Simple and Compound Both Question 12 Detailed Solution

Here P = 4500 , T = 8 , R = 8%

Simple interest = (P × R × T)/100, where P is the principal, R is the rate of interest and T is the time period.

Compound interest = [P (1 + R/100)ⁿ] - P, where P is the principal, R is the rate of interest and n is the time period.

⇒ SI = (4500 × 8 × 3)/100 = Rs. 1080

⇒ CI = [4500 (1 + 8/100)³] - 4500 = Rs. 5668.7 - 4500 = 1168.7

∴ Required difference = Rs. 88.70

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Simple and Compound Both Question 13

1. Rs. 100,000
2. Rs. 150,000
3. Rs. 160,000
4. Rs. 200,000

Simple and Compound Both Question 13 Detailed Solution

Given:

Rate = 15 %

Difference between CI and SI in 2 years= Rs. 3375

Time = 2 years

Concept:

CI –SI = P× (R/100)²

Calculation:

⇒ 3375 = P× (15/100)²

⇒ P = 150000

∴ The required result will be 150,000

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Simple and Compound Both Question 14

1. Rs. 1260
2. Rs. 1500
3. Rs. 1200
4. Rs. 1300
5. Rs. 1320

Simple and Compound Both Question 14 Detailed Solution

Given:

Principal amount = P

Number of years = 4

S.I = 1200

Amount on C.I =Amount onS.I + 60

Formula used:

Amount = Principal + Interest

Calculation:

Amount onS.I = 1200 + P

⇒Amount on C.I = (1200 + P) + 60

⇒Amount on C.I = 1260 + P

Now,

Amount on C.I = P + C.I

⇒ C.I = Amount on C.I - P

⇒ C.I = 1260 + P - P

⇒ C.I = 1260

∴ Compound interest accrued = Rs.1260

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Simple and Compound Both Question 15

1. 322400
2. 392400
3. 592400
4. 398400

Simple and Compound Both Question 15 Detailed Solution

Given:

Difference between Compound Interest (C.I.) and Simple Interest (S.I.) = Rs. 981.

Time period (T) = 2 years.

Rate (R) = 5% per annum.

Concept used:

For principal (P), rate percent per annum (R%)and time (T),

S.I. = P× R× T / 100.

For C.I.,

Amount = P + C.I.

Amount = P(1 + R / 100)^T

Solution:

We first calculate S.I. as:

S.I. = P× R× T / 100

S.I. = P× 5× 2 / 100

S.I. = 10P / 100.

Now, we calculate amount in C.I. as:

Amount =P(1 + R / 100)T

Amount = P(1 + 5 / 100)²

Amount = P(1 + 1 / 20)²

Amount = P(21 / 20)(21 / 20)

Amount = 441P / 400.

Thus,

Amount = P + C.I.

C.I. = Amount - P

C.I. = (441P / 400) - P

C.I. = (441P - 400P)/ 400

C.I. = 41P / 400.

Difference between S.I. and C.I.

(41P / 400) - (10P / 100) = 981

(41P - 40P) / 400 = 981

P / 400 = 981

P = 981×400

P = 392400.

∴ The sum is Rs. 392400.

Shortcut Trick

Direct formula to solve such questions:

Difference = P × (R / 100)²

where P = Principal

R = rate percent per annum

Using this formula we can solve the given question as:

Difference = P × (R / 100)²

981 = P × (5 / 100) (5 / 100)

P = 981 × 100 × 100 / 25P = 981× 400
P = 392400.

∴ The sum is Rs. 392400.

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