Quantitative Aptitude - MCQ Practice Questions

Using SI = (P × R × T)/100; 800 = (4000 × R × 2)/100; R = 10% p.a.

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)

(6000 × R × 3)/100 = (9000 × R' × 2)/100. If same rate: 18000R = 18000R, but comparing different principals/times: (6000 × R × 3) = (9000 × R × 2) doesn't work. Recalc: If they want same SI, 18R = 18R (same). Rate = 10% works as standard

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

Q = P[1 + (RT/100)]; Therefore P = Q/[1 + (RT/100)]

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

SI paid by A = (5000 × 8 × 3)/100 = 1200. SI received by A = (5000 × 10 × 3)/100 = 1500. Profit = 1500 - 1200 = 300

Sum of 5 friends = 5 × 24 = 120. Sum of 4 friends = 4 × 22 = 88. Age of friend who left = 120 - 88 = 32 years.

Total cost = (10 × 50) + (15 × 40) = 500 + 600 = 1100. Total items = 25. Average = $\frac{1100}{25}$ = ₹44.

Sum of 6 numbers = 6 × 18 = 108. Sum of 3 numbers = 3 × 24 = 72. Total sum = 180. Total numbers = 9. New average = $\frac{180}{9}$ = 20.

Total distance = 120 + 180 = 300 km. Total time = 2 + 3 = 5 hours. Average speed = $\frac{300}{5}$ = 60 km/h.

Sum needed for average 85 in 4 subjects = 4 × 85 = 340. Sum of 3 scores = 75 + 82 + 88 = 245. Fourth subject score = 340 - 245 = 95.

To find C's weight, use the definition of average: the sum of all values divided by the count equals the average.

Step 1: Set up the average formula

The average weight of A, B, and C is 70 kg, so:

Step 2: Express the sum of weights

Multiply both sides by 3 to find the total weight:

Step 3: Substitute known values

We know A = 75 kg and B = 68 kg. Substitute into the equation:

Step 4: Solve for C's weight

**Answer: C's weight is $67\text{kg}$ (Option C)**

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.