Quantitative Aptitude - MCQ Practice Questions

Step 1: Population increase = 8% of 50,000 = 0.08 × 50,000 = 4,000.

Step 2: Current population = 50,000 + 4,000 = 54,000.

Therefore, option B is correct.

Step 1: Percentage spent on rent and food = 35% + 20% = 55%.

Step 2: Amount spent = 55% of ₹45,000 = 0.55 × 45,000 = ₹24,750.

Therefore, option A is correct.

Step 1: Profit = 25% of ₹400 = 0.25 × 400 = ₹100.

Step 2: Selling Price = Cost Price + Profit = 400 + 100 = ₹500.

Step 3: Let Marked Price = M.

After 15% discount: M × (1 - 0.15) = 500, so M × 0.85 = 500, M = $\frac{500}{0}$.85 = ₹588.24 (approximately).

Therefore, option A is correct.

Step 1: After 12% increase: Price = 500 × (1 + 0.12) = 500 × 1.12 = ₹560.

Step 2: After 10% decrease: Price = 560 × (1 - 0.10) = 560 × 0.90 = ₹504.

Therefore, option B is correct.

Step 1: Reduction in production = 18% of 5,000 = 0.18 × 5,000 = 900 units.

Step 2: Current production = 5,000 - 900 = 4,100 units per day.

Therefore, option C is correct.

Step 1: Profit = Selling Price - Cost Price = 312 - 240 = ₹72.

Step 2: Profit% = (Profit/CP) × 100 = ($\frac{72}{240}$) × 100 = 30%.

So option B is correct.

Step 1: Loss = 15% of CP = 15% of 500 = ₹75.

Step 2: Selling Price = CP - Loss = 500 - 75 = ₹425 per kg.

So option B is correct.

Step 1: Marked Price = ₹800, Discount = 12% of 800 = ₹96.

Step 2: Selling Price = 800 - 96 = ₹704.

Step 3: Profit = 704 - 600 = ₹104.

Step 4: Profit% = ($\frac{104}{600}$) × 100 = 17.33% ≈ 16%.

So option C is correct.

Step 1: Total CP = 50 × 40 = ₹2000.

Step 2: 80% of 50 = 40 kg sold at ₹50/kg = ₹2000, remaining 10 kg at ₹35/kg = ₹350.

Step 3: Total SP = 2000 + 350 = ₹2350.

Step 4: Profit% = ($\frac{350}{2000}$) × 100 = 17.5% ≈ 20%.

So option C is correct.

Step 1: Item A: SP = 400 + (25% of 400) = 400 + 100 = ₹500.

Step 2: Item B: SP = 400 - (18% of 400) = 400 - 72 = ₹328.

Step 3: Total CP = 800, Total SP = 828.

Step 4: Profit% = ($\frac{28}{800}$) × 100 = 3.5%.

So option A is correct.

Step 1: CP = ₹5000.

Step 2: Marked Price = 5000 + (60% of 5000) = 5000 + 3000 = ₹8000.

Step 3: Discount = 20% of 8000 = ₹1600.

Step 4: SP = 8000 - 1600 = ₹6400.

Step 5: Profit% = ($\frac{1400}{5000}$) × 100 = 28%.

So option A is correct.

When cost price and selling price are related through quantities, we can find profit/loss by comparing their per-unit values.

Step 1: Set Up the Given Relationship

We're told that the cost price of 18 items equals the selling price of 15 items. Let's denote the cost price per item as CP and selling price per item as SP.

Step 2: Find the Ratio of Selling Price to Cost Price

Rearranging the equation to find the relationship between SP and CP:

Step 3: Calculate Profit Percentage

Since SP > CP, there is a profit. The profit percentage is calculated as:

The profit percentage is 20%, so the answer is (B) 20% profit.

Step 1: CP of 3 articles = ₹100, so CP of 1 article = $\frac{100}{3}$.

Step 2: SP of 2 articles = ₹100, so SP of 1 article = $\frac{100}{2}$ = ₹50.

Step 3: Profit on 1 article = 50 - $\frac{100}{3}$ = $\frac{150}{3}$ - $\frac{100}{3}$ = $\frac{50}{3}$.

Step 4: Profit% = ($\frac{50}{3}$)/($\frac{100}{3}$) × 100 = ($\frac{50}{100}$) × 100 = 50%.

So option B is correct.

Step 1: After 15% discount: 2000 - (15% of 2000) = 2000 - 300 = ₹1700.

Step 2: After 10% discount on ₹1700: 1700 - (10% of 1700) = 1700 - 170 = ₹1530.

Step 3: This is the SP.

If profit is 20%, then SP = CP × 1.2, so 1530 = CP × 1.2.

Step 4: CP = $\frac{1530}{1}$.2 = ₹1275 ≈ ₹1300.

So option B is correct.

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

Step 2: SI = (8000 × 6 × 3) / 100 = $\frac{144000}{100}$ = ₹1440.

Step 3: Total Amount = Principal + SI = 8000 + 1440 = ₹9440.

Step 1: SI = Amount - Principal = 6500 - 5000 = ₹1500.

Step 2: Use SI = (P × R × T) / 100, so 1500 = (5000 × R × 5) / 100.

Step 3: 1500 = 250R, therefore R = $\frac{1500}{250}$ = 6% per annum.

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: We need SI = P, so SI = ₹12000.

Step 2: Using SI = (P × R × T) / 100, we get 12000 = (12000 × 8 × T) / 100.

Step 3: 12000 = 960T, therefore T = $\frac{12000}{960}$ = 12.5 years.

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)