Quantitative Aptitude - MCQ Practice Questions

In simple interest problems, the difference in amounts over different time periods reveals the interest earned, which we can use to find the principal and rate.

Step 1: Find the interest earned between the two periods

The amount after 2 years is ₹7,200 and after 3.5 years is ₹8,400.

Step 2: Calculate the annual simple interest rate

Since ₹1,200 is earned in 1.5 years, the annual interest is:

Step 3: Find the principal using the first condition

Using the simple interest formula: $A=P+I$, where $A$ is the amount, $P$ is the principal, and $I$ is total interest.

After 2 years:

Step 4: Verify with the second condition

After 3.5 years, total interest = $800\times 3.5=₹2,800$

Amount = $5,600+2,800=₹8,400$ ✓

Answer: The principal amount is ₹5,600 (Option D)

To find out who earned more interest, we calculate the simple interest for both Suresh and Amit using the formula:

1. Calculate Suresh's Interest:Principal ($P$) = ₹15,000Rate ($R$) = $7\%$Time ($T$) = $1.5$ years

2. Calculate Amit's Interest:Principal ($P$) = ₹12,000Rate ($R$) = $9\%$Time ($T$) = $2$ years

3. Comparison:Amit's interest: ₹2160Suresh's interest: ₹1575Since $₹2160>₹1575$, Amit earned more interest.

Amit earned more interest, by ₹585.

Simple interest is calculated as a percentage of the principal amount and remains constant each year, making it easier to compare different investment schemes.

Step 1: Calculate Maturity Amount for Scheme A

For Scheme A, we apply the simple interest formula where Principal = ₹20,000, Rate = 6% per annum, and Time = 4 years.

Step 2: Calculate Maturity Amount for Scheme B

For Scheme B, we apply the simple interest formula where Principal = ₹20,000, Rate = 5.5% per annum, and Time = 5 years.

Step 3: Compare the Maturity Amounts

To find which scheme is better and by how much, we subtract the smaller amount from the larger amount.

Since ₹25,500 > ₹24,800, Scheme B gives ₹700 more than Scheme A.

The answer is (C) Scheme B gives ₹700 more than Scheme A.

Step 1: Calculate SI = (P × R × T) / 100 = (12,000 × 7.5 × 4) / 100 = 360,$\frac{000}{100}$ = ₹3,600.

Step 2: Amount = Principal + SI = 12,000 + 3,600 = ₹15,600.

Option A is correct.

Let sum = P.

Step 1: SI₁ = (P × 9 × 5) / 100 = 45P/100.

Step 2: SI₂ = (P × 6 × 8) / 100 = 48P/100.

Step 3: Difference = 48P/100 - 45P/100 = 3P/100 = 840.

Step 4: P = 84,$\frac{000}{3}$ = ₹2,000.

Option A is correct.

Step 1: Extra interest earned on ₹5,000 in 4 years = ₹1,200.

Step 2: Using SI = (P × R × T) / 100, we have 1,200 = (5,000 × R × 4) / 100.

Step 3: 1,200 = 200R.

Step 4: R = 1,$\frac{200}{200}$ = 6% p.a.

Option B is correct.

In simple interest, the amount grows linearly with time. The key is to find how much interest accrues per year, then work backward to find the principal.

Step 1: Find the interest earned between year 2 and year 4

The amount after 2 years is ₹4200, and after 4 years is ₹4800.

In 2 years (from year 2 to year 4), the interest earned is:

Step 2: Calculate annual simple interest

Since simple interest is constant each year:

Step 3: Find total interest in first 2 years

If the annual interest is ₹300, then in 2 years:

Step 4: Calculate the principal

Using the formula: $\text{Amount}=\text{Principal}+\text{Simple Interest}$

Verification: Principal ₹3600 at SI of ₹300/year gives ₹4200 in 2 years ✓ and ₹4800 in 4 years ✓

Answer: The principal is ₹3600 (Option B)

Step 1: SI for first 2 years = (15000 × 10 × 2) / 100 = ₹3000.

Step 2: After 2 years, remaining principal = 15000 - 3000 = ₹12000.

Step 3: SI on ₹12000 for 1 year = (12000 × 10 × 1) / 100 = ₹1200.

Step 4: Total SI = 3000 + 1200 + ₹1500 (interest on ₹3000 for 1 year) = ₹5700.

We use the simple interest formula $I=\frac{P\times R\times T}{100}$ to find interest on equal principal amounts invested at different rates and periods, then set up an equation using the given difference.

Step 1: Write the interest formula for each investment

Let the principal be $P$ (same for both).

For Investment 1 (12% p.a. for 4 years):

For Investment 2 (15% p.a. for 3 years):

Step 2: Find the difference in interests

Since $I_1>I_2$ (higher rate × longer time):

Step 3: Use the given difference to find P

We're told the difference is ₹540:

Step 4: Verify the answer

$I_1=0.48\times 18000=8640$

$I_2=0.45\times 18000=8100$

Difference: $8640-8100=540$ ✓

Let each principal amount be P.

Using Simple Interest formula:

SI=

100

P×R×T

​

First investment

SI

1

​

=

100

P×12×4

​

=

100

48P

​

Second investment

SI

2

​

=

100

P×15×3

​

=

100

45P

​

Difference in interests:

100

48P

​

−

100

45P

​

=540

100

3P

​

=540

3P=54000

P=18000

Therefore, each principal amount is ₹18,000.

Answer: Each principal amount is ₹18,000 (Option B)

Amount = P + (P × R × T)/100; 9200 = P + (P × 8 × 4)/100; 9200 = P(1 + 0.32); P = 7000

Let sum = P. Difference in SI = (P × 12 × 3)/100 - (P × 10 × 3)/100 = (6P)/100 = 600; P = 10000

17600 = P(1 + (11 × 4)/100); 17600 = P(1.44); P = 12222.22 ≈ 12000 (approx)

SI = 33250 - 25000 = 8250. Using T = (SI × 100)/(P × R) = (8250 × 100)/(25000 × 9) = 3.67 ≈ 3.5 years

We use the simple interest formula $SI=\frac{P\times R\times T}{100}$ to equate the interests earned on both parts.

Step 1: Set up variables

Let the first part be $x$ and the second part be $(12000-x)$.

Step 2: Write the simple interest formula for each part

Simple interest on first part at 10% for 2 years:

Simple interest on second part at 12% for 2 years:

Step 3: Equate the interests

Given that both simple interests are equal:

Step 4: Solve for x

Answer: The first part is ₹6,545.45 (Option B)

SI = 10240 - 8000 = 2240. Rate = (2240 × 100)/(8000 × 4) = 7% p.a.

Simple interest is calculated as a percentage of the principal amount and remains constant each year.

Step 1: Calculate Interest for Friend 1 (8% rate)

Friend 1 invested ₹10,000 at 8% simple interest for 3 years.

Step 2: Calculate Interest for Friend 2 (10% rate)

Friend 2 invested ₹10,000 at 10% simple interest for 3 years.

Step 3: Calculate Interest for Friend 3 (12% rate)

Friend 3 invested ₹10,000 at 12% simple interest for 3 years.

Step 4: Calculate Total Interest

Add the interest earned by all three friends.

The total interest earned by all three friends is ₹9,000.

Answer: (A) ₹9,000

Using T = (SI × 100)/(P × R) = (3750 × 100)/(15000 × 7.5) = 3 years