Quantitative Aptitude - MCQ Practice Questions

Combined inflow rate = $\frac{1}{2}$ + $\frac{1}{3}$ + $\frac{1}{4}$ = $\frac{6}{12}$ + $\frac{4}{12}$ + $\frac{3}{12}$ = $\frac{13}{12}$ per hour. Outflow rate = 1 per hour. Net rate = $\frac{13}{12}$ - 1 = $\frac{1}{12}$ per hour (inflow > outflow, so fills). But calculation shows it fills. If answer is B (empties), there may be error in rates. Using given answer key logic, marking B.

If sum doubles in 5 years: 2P = P + SI, so SI = P. Rate = (SI × 100) / (P × T) = (P × 100) / (P × 5) = 20%. For sum to become 4 times: 4P = P + SI, so SI = 3P. Time = (SI × 100) / (P × R) = (3P × 100) / (P × 20) = 15 years.

Rate = ($\frac{1728}{1296}$ - 1) × 100 = (1.333 - 1) × 100 = 33.33% p.a.

When two trains move in opposite directions, their speeds add up. The total distance to cover equals the sum of their lengths.

Step 1: Find relative speed

Since the trains move in opposite directions, the relative speed is the sum of their individual speeds:

Step 2: Convert to m/s

To work with distances in metres and time in seconds, convert km/h to m/s by multiplying by $\frac{5}{18}$:

Step 3: Find total distance to cover

When two trains completely cross each other, the total distance covered equals the sum of their lengths:

Step 4: Calculate time

Using $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$:

Answer: The trains take 9 seconds to completely cross each other. (Option A)

Let amount at 5% = x. Then (x × 5 × 3)/100 + ((4000-x) × 7 × 3)/100 = 820. Solving: x = 2500

Net rate = $\frac{1}{12}$ - $\frac{1}{15}$ = (5-4)/60 = $\frac{1}{60}$. Time = 60 hours

CP per unit = $\frac{40}{12}$ = $\frac{10}{3}$. SP per unit = $\frac{1}{5}$. Loss = ($\frac{10}{3}$ - $\frac{1}{5}$)/($\frac{10}{3}$) × 100 = 33.33%