Quantitative Aptitude - MCQ Practice Questions

x% of 480 = 72, so x = 15%. For 96: ($\frac{96}{480}$) × 100 = 20%

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

Upstream speed = $\frac{50}{5}$ = 10 km/h. Downstream speed = $\frac{80}{4}$ = 20 km/h. Boat speed in still water = (10 + 20)/2 = 15 km/h.

To find the time taken when both pipes work together, use the concept of work rates: the combined rate equals the sum of individual rates.

Step 1: Find individual work rates

Pipe A fills the tank in 12 hours, so its rate is $\frac{1}{12}$ tank per hour.

Pipe B fills the tank in 15 hours, so its rate is $\frac{1}{15}$ tank per hour.

Step 2: Find combined work rate

When both pipes work together:

Find the LCM of 12 and 15, which is 60:

Step 3: Calculate time to fill one tank

If the combined rate is $\frac{3}{20}$ tank per hour, then time to fill 1 tank is:

Step 4: Convert to hours and minutes

**Answer: Both pipes together fill the tank in $6$ hours and $40$ minutes (Option B)**

# Average Cost Calculation in Profit-Loss Problems

To find the average cost, we need to calculate the total amount spent on all goods and divide by the total quantity of goods purchased.

Step 1: Calculate Selling Price of First Transaction

The merchant bought goods for ₹10,000 and sold them at 20% profit, but we need the total cost invested.

Step 2: Calculate Actual Cost of Second Transaction

The merchant bought goods for ₹15,000 at a 10% loss, meaning ₹15,000 is the selling price, not cost price.

Step 3: Calculate Average Cost

The average cost is the total amount spent divided by the number of transactions (treating each purchase as one unit).

Note: Given the answer options, the question likely interprets "average cost" as the mean of the two transaction amounts: ₹(10,000 + 15,000)/2 = ₹12,500

Final Answer: (D) ₹12,500

For consecutive odd numbers, the average equals the middle (4th) number. So 4th number = 39. The 7 numbers are: 33, 35, 37, 39, 41, 43, 45. Largest = 45.

Distance in first 2 hours = 50 × 2 = 100 km (which is 25% of total). Total distance = 400 km. Total time at 60 km/h = $\frac{400}{60}$ = 6.67 hours.

Interest on first = 5,000 × 8 × $\frac{2}{100}$ = 800. Interest on second = 7,500 × 12 × $\frac{2}{100}$ = 1,800. Total interest = 2,600. Average rate = (2,600 × 100) / (12,500 × 2) = 10.4%.

Increase in total age = 38 - 28 = 10. If average increases by 2, then group size = $\frac{10}{2}$ = 5.

When equal quantities are mixed, average concentration = (40 + 50 + 60)/3 = $\frac{150}{3}$ = 50%.

CP of 3 items at 20% profit: 3 × ($\frac{200}{1}$.2) = 500. CP of 2 items at 25% loss: 2 × ($\frac{300}{0}$.75) = 800. Total CP = 1300, Total SP = 1500. Profit% = ($\frac{200}{1300}$) × 100 = 15.$\frac{38}{3}$.58 ≈ 4.29%.

Initial average age × 6 = Total. New average = (Initial average + 2). Change in total = 6 × 2 = 12. New person's age = 40 + 12 = 52 years.

CP = 100 × 50 = 5000. SP of 60 at 20% profit = 60 × 50 × 1.2 = 3600. SP of 40 at 10% loss = 40 × 50 × 0.9 = 1800. Total SP = 5400. Profit = 400. Profit% = ($\frac{400}{5000}$) × 100 = 8%.