Quantitative Aptitude - MCQ Practice Questions

When traveling downstream and upstream, the boat's effective speed changes due to the current's aid or resistance.

Step 1: Calculate Downstream Speed

Downstream, the current aids the boat's motion, so we add the current speed to the boat's speed in still water.

Step 2: Calculate Time for Downstream Journey

Using the formula: Time = Distance ÷ Speed, we find the time to travel 108 km downstream.

Step 3: Calculate Upstream Speed

Upstream, the current opposes the boat's motion, so we subtract the current speed from the boat's speed in still water.

Step 4: Calculate Time for Upstream Journey

The boat must return the same 108 km against the current.

Step 5: Calculate Total Time

Add the downstream and upstream times to get the total journey time.

The answer is 15 hours.

To solve this problem, we use the concept of work rates: if A completes work in 10 days, A's rate is $\frac{1}{10}$ of the work per day, and similarly for B.

Step 1: Find individual work rates

A completes the work in 10 days, so A's rate = $\frac{1}{10}$ work/day

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

Step 2: Calculate work done together in 3 days

Combined rate when working together:

Work completed in 3 days:

Step 3: Find remaining work

Step 4: Calculate days B needs to finish alone

B works alone at rate $\frac{1}{15}$ work/day. For remaining work $\frac{1}{2}$:

Answer: B will take 7.5 more days to finish the work (Option C)

Profit per unit = 100 - 75 = 25. Profit% = ($\frac{25}{75}$) × 100 = 33.33%

When two trains move towards each other, their relative speed is the sum of their individual speeds, and they must cover the combined length of both trains to completely pass each other.

Step 1: Find the relative speed

Since the trains are moving towards each other, we add their speeds:

Step 2: Convert relative speed to m/s

To work with the lengths given in meters, convert km/h to m/s by multiplying by $\frac{5}{18}$:

Step 3: Find the total distance to be covered

For the trains to completely pass each other, the total distance covered equals the sum of their lengths:

Step 4: Calculate time using distance = speed × time

**Answer: The trains will take $18$ seconds to completely pass each other. (Option A)**

If B = 100, A = 80. Increase needed = 20. Percentage = ($\frac{20}{80}$) × 100 = 25%

Rate A = $\frac{1}{20}$, Rate B = $\frac{1}{30}$. Combined = $\frac{5}{60}$. In 10 hours = $\frac{50}{60}$. Remaining = $\frac{10}{60}$. B's time = ($\frac{10}{60}$)/($\frac{1}{30}$) = 5 hours

A = P + SI = P + (P × 10 × 2)/100 = P × 1.2. 2420 = P × 1.2. P = 2000

Let CP = 100. MP = 150. SP = 150 × 0.8 = 120. Profit% = 20%

A = P(1 + R/100)^T. 3600 = P(1.1)^3 = P(1.331). P = $\frac{3600}{1}$.331 ≈ Rs. 2703.67.

Let CP = 100. MP = 140. SP = 140 × 0.9 = 126. Profit% = (126-100)/100 × 100 = 26%.

Let B's income = 100, A's = 125. B's is less by $\frac{25}{125}$ × 100 = 20%.

If $\frac{1}{3}$ work = 5 days, then full work = 5 × 3 = 15 days.

Combined rate = $\frac{1}{8}$. P's rate = $\frac{1}{12}$. Q's rate = $\frac{1}{8}$ - $\frac{1}{12}$ = $\frac{1}{24}$. Q takes 24 days.

Speed = $\frac{240}{4}$ = 60 km/h = 60 × $\frac{5}{18}$ = 16.67 m/s.

Upstream speed = $\frac{30}{6}$ = 5 km/h. Downstream = $\frac{30}{3}$ = 10 km/h. Stream speed = (10-5)/2 = 2.5 km/h.

A = 5000(1.12)^2 = 5000 × 1.2544 = Rs. 6272.

If $\frac{1}{4}$ tank = 3 hours, full tank = 3 × 4 = 12 hours.

CP = 50 × 8 = 400. SP = 50 × 10 = 500. Profit% = (500-400)/400 × 100 = 25%.

Net rate = $\frac{1}{12}$ + $\frac{1}{15}$ - $\frac{1}{20}$ = $\frac{5}{60}$ + $\frac{4}{60}$ - $\frac{3}{60}$ = $\frac{6}{60}$ = $\frac{1}{10}$. Time = 10 hours

Combined rate = $\frac{1}{20}$ + $\frac{1}{30}$ = $\frac{3}{60}$ + $\frac{2}{60}$ = $\frac{5}{60}$ = $\frac{1}{12}$. Time = 12 days