Quantitative Aptitude - MCQ Practice Questions

Average speed is the total distance traveled divided by the total time taken, calculated as $\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}$.

Step 1: Calculate total distance

The train travels in two segments:

Step 2: Calculate total time

The train travels for two different periods:

Step 3: Apply the average speed formula

Step 4: Simplify the division

Total distance traveled:

200+150=350 km

Total time taken:

4+2.5=6.5 hours

Average speed:

Average Speed=

Total Time

Total Distance

​

=

6.5

350

​

=

13

700

​

≈53.85 km/h

Therefore, the average speed is approximately 53.85 km/h.

**Answer: The average speed is approximately $53.85\text{ km/h}$ (Option C)**

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

Rate of worker 1 = $\frac{1}{8}$, worker 2 = $\frac{1}{12}$. Combined rate = $\frac{1}{8}$ + $\frac{1}{12}$ = (3+2)/24 = $\frac{5}{24}$. Time = $\frac{24}{5}$ = 4.8 days.

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%.

Total height of 5 = 165 × 5 = 825 cm. After adding 180 cm: 825 + 180 = 1005 cm. New average = $\frac{1005}{6}$ = 167.5 cm.

For equal distances, average speed = 3/($\frac{1}{40}$ + $\frac{1}{50}$ + $\frac{1}{60}$) = 3/((3+2.4+2)/120) = 3/(7.$\frac{4}{120}$) = $\frac{360}{7}$.4 = 48.65 ≈ 49.09 km/h. Using LCD: 3/((15+12+10)/600) = $\frac{1800}{37}$ ≈ 48.65 km/h.

Total income of 4 = 45000 × 4 = 180000. After 5th employee: 180000 + 55000 = 235000. New average = $\frac{235000}{5}$ = 47000.

Let current speed = c. Upstream speed = 15 - c, downstream = 15 + c. Distance = 4(15-c) = 2(15+c). 60 - 4c = 30 + 2c. 30 = 6c. c = 5 km/h.

Sum of 5 numbers = 48 × 5 = 240. Sum of 4 numbers = 40 + 45 + 50 + 55 = 190. Fifth number = 240 - 190 = 50.

Profit per unit = $\frac{2500}{50}$ = 50. This remains constant regardless of quantity. Average profit per unit = ₹50.

Profit per article = 120 - 80 = ₹40. Profit percentage = ($\frac{40}{80}$) × 100 = 50%. This remains constant for any number of articles, so average profit = 50%.

Combined rate = $\frac{1}{30}$ + $\frac{1}{20}$ = $\frac{5}{60}$ = $\frac{1}{12}$. Time to fill full tank = 12 hours. Time to fill $\frac{2}{5}$ tank = 12 × $\frac{2}{5}$ = 4.8 hours. Average per pipe = 4.8 × 1.5 = 7.2 hours.

SI = (P × R × T) / 100 = (15,000 × 12 × 2) / 100 = ₹3,600. Average per year = 3,$\frac{600}{2}$ = ₹1,800.

For equal distances, average speed = 2ab/(a+b) = (2 × 8 × 12)/(8 + 12) = $\frac{192}{20}$ = 9.6 km/h.

Let total distance = 400 km. Distance segments: 100 km at 50 km/h (2 hrs), 200 km at 60 km/h (3.33 hrs), 100 km at 75 km/h (1.33 hrs). Total time ≈ 6.66 hrs. Average speed = $\frac{400}{6}$.66 ≈ 60.8 km/h.

To find the average work rate per day for the remaining workers, we must calculate each worker's individual rate, then find the combined rate after A leaves.

Step 1: Calculate individual work rates

Worker A completes the job in 12 days, so A's rate = $\frac{1}{12}$ job/day

Worker B completes the job in 15 days, so B's rate = $\frac{1}{15}$ job/day

Worker C completes the job in 20 days, so C's rate = $\frac{1}{20}$ job/day

Step 2: Find the combined rate of all three workers

Finding the LCM of 12, 15, and 20:

Step 3: Calculate work done in first 2 days

In 2 days, all three workers complete:

This information establishes context, but the question asks for the average rate of remaining workers (B and C) after A leaves.

Step 4: Find average work rate of remaining workers (B and C)

Number of remaining workers = 2

**Answer: The average work rate per day for the remaining workers is $\frac{7}{120}$ (Option A)**

[The key to solving this problem is finding the total revenue from all items, subtracting the revenue from the 2 discounted items, and then dividing by the remaining quantity.]

Step 1: Find the Total Selling Price of All 8 Items

The average selling price is given as ₹250 for 8 items, so we multiply to find the total.

Step 2: Calculate the Selling Price of the 2 Items Sold at ₹180 Each

Two items were sold at ₹180 each, so we find their combined revenue.

Step 3: Find the Total Selling Price of Remaining 6 Items

Subtract the revenue from the 2 discounted items from the total revenue.

Step 4: Calculate the Average Price of the Remaining 6 Items

Divide the total price of 6 items by the quantity.

The average price of the remaining 6 items is ₹273.33.

The answer is (A) ₹273.33

In ratio 3:2, total parts = 5. Cost = (3 × 40 + 2 × 60)/5 = (120 + 120)/5 = $\frac{240}{5}$ = ₹48 per kg.