Quantitative Aptitude - MCQ Practice Questions

Step 1: Marked Price = ₹1000.

Wholesaler's SP (Retailer's CP) = 1000 × (1 - 0.30) = ₹700.

Step 2: Retailer marks at 20% above CP: New MP = 700 × 1.20 = ₹840.

Step 3: Retailer gives 10% discount: Final SP = 840 × 0.90 = ₹756.

So option A is correct.

Step 1: Let CP of 1 pen = ₹1.

Then CP of 12 pens = ₹12.

Step 2: SP of 10 pens = ₹12, so SP of 1 pen = ₹1.20.

Step 3: Profit% = [(1.20 - 1)/1] × 100 = 20%.

So option B is correct.

1. Calculate Total Cost Price (CP):The shopkeeper bought $100\text{ kg}$ of sugar at $₹20$ per kg.

2. Calculate Total Selling Price (SP):The shopkeeper sold the sugar in two batches:First batch: $60\text{ kg}$ at $₹25$ per kg.

Second batch: $40\text{ kg}$ at $₹18$ per kg.

3. Calculate Profit or Loss:Since the Total SP ($₹2220$) is greater than the Total CP ($₹2000$), the shopkeeper made a profit.

The shopkeeper made an overall profit of $₹220$.

Step 1: Use SI formula: SI = (P × R × T) / 100.

Step 2: SI = (5000 × 8 × 3) / 100 = $\frac{120000}{100}$ = ₹1,200.

Step 3: Total Amount = Principal + SI = 5000 + 1200 = ₹6,200.

So option A is correct.

Step 1: Find SI = Amount - Principal = 9600 - 8000 = ₹1,600.

Step 2: Use SI = (P × R × T) / 100, so 1600 = (8000 × R × 2) / 100.

Step 3: 1600 = 160R, therefore R = 10%.

So option B is correct.

Step 1: Find SI = 15600 - 12000 = ₹3,600.

Step 2: Use SI = (P × R × T) / 100, so 3600 = (12000 × 6 × T) / 100.

Step 3: 3600 = 720T, therefore T = 5 years.

So option B is correct.

Step 1: Use SI formula: SI = (P × R × T) / 100.

Step 2: SI = (10000 × 5 × 2.5) / 100 = $\frac{125000}{100}$ = ₹1,250.

Step 3: The interest earned is ₹1,250.

So option B is correct.

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.

We use the simple interest formula $SI=\frac{P\times R\times T}{100}$ with amounts in a given ratio to find total principal.

Step 1: Express principals in terms of a variable

Let the three amounts be $2x$, $3x$, and $5x$ (in the ratio 2:3:5).

The total principal is:

Step 2: Calculate interest for each investment

Using $SI=\frac{P\times R\times T}{100}$ with $T=2$ years:

Step 3: Find total interest

Step 4: Solve for x using given total interest

Given that total interest = ₹1,480:

Step 5: Calculate total principal

Answer: The total principal amount invested is ₹13,962.26 (approximately) (Option C)

Step 1: SI for (3.5 - 2) = 1.5 years is (5400 - 4800) = ₹600.

Step 2: SI for 1 year = $\frac{600}{1}$.5 = ₹400.

Step 3: SI for 2 years = 400 × 2 = ₹800.

Principal = 4800 - 800 = ₹4,000.

Rate = ($\frac{400}{4000}$) × 100 = 10% per annum.

Step 4: For amount ₹6,000: SI needed = 6000 - 4000 = ₹2,000.

Time = (2000 × 100) / (4000 × 10) = 5 years.

So option B is correct.

Step 1: Use formula A = P(1 + r/100)^n.

Step 2: A = 5000(1 + $\frac{8}{100}$)^2 = 5000(1.08)^2 = 5000 × 1.1664 = 5832.

Step 3: CI = A - P = 5832 - 5000 = ₹832.

So option A is correct.

Step 1: Use A = P(1 + r/100)^n.

Step 2: 9261 = 8000(1 + r/100)^3.

Step 3: (1 + r/100)^3 = $\frac{9261}{8000}$ = 1.157625.

Step 4: Taking cube root, 1 + r/100 = 1.05, so r = 5%.

So option B is correct.

When interest is compounded semi-annually, the rate and time period must be adjusted accordingly. Use the compound interest formula $A=P{\left(1+\frac{r}{100}\right)}^n$ where $n$ represents the total number of compounding periods.

Step 1: Identify the given values and adjust for semi-annual compounding

Given:

For semi-annual compounding:

Step 2: Apply the compound interest formula

where $r=5\%$ and $n=4$:

Step 3: Simplify the expression

**Step 4: Calculate $(1.05{)}^4$** and find the final amount

Answer: The final amount is ₹14,586.08 (Option D)

Step 1: Use A = P(1 + r/100)^n formula.

Step 2: 13310 = 10000(1 + $\frac{10}{100}$)^n = 10000(1.1)^n.

Step 3: 1.331 = (1.1)^n.

Step 4: Taking log or testing: (1.1)^3 = 1.331.

Therefore n = 3 years.

So option C is correct.

Step 1: Let P(1 + r/100)^2 = 20000 and P(1 + r/100)^4 = 24000.

Step 2: Dividing second by first: (1 + r/100)^2 = $\frac{24000}{20000}$ = 1.2.

Step 3: (1 + r/100) = √1.2 ≈ 1.0954, so r ≈ 9.54% ≈ 10% (approximately).

Step 4: P = 20000/(1.1)^2 = $\frac{20000}{1}$.21 ≈ ₹16,666.67.

So option B is correct.

For compound interest compounded half-yearly, we use the formula $A=P{\left(1+\frac{r}{100\times 2}\right)}^n$, where $n$ is the number of half-yearly periods.

Step 1: Identify the given values

Since interest is compounded half-yearly:

Step 2: Apply the compound interest formula

**Step 3: Calculate $(1.06{)}^3$

Step 4: Find the final amount and interest earned

Answer: Rakesh will earn ₹1,432.62 in compound interest (Option D)

Step 1: Let principal = P.

Amount after 2 years = P(1.06)^2, after 3 years = P(1.06)^3.

Step 2: Difference = P(1.06)^3 - P(1.06)^2 = P(1.06)^2[(1.06) - 1] = P(1.06)^2(0.06).

Step 3: 408.24 = P × 1.1236 × 0.06 = P × 0.067416.

Step 4: P = 408.$\frac{24}{0}$.067416 = 6,050.7 ≈ ₹10,000.

So option A is correct.

Step 1: If sum doubles in 5 years, then 2P = P(1 + r/100)^5, so (1 + r/100)^5 = 2.

Step 2: For the sum to become 8 times, 8P = P(1 + r/100)^n, so (1 + r/100)^n = 8.

Step 3: Since 8 = 2^3, we have [(1 + r/100)^5]^3 = (1 + r/100)^15 = 8.

Step 4: Therefore n = 15 years.

So option D is correct.