Quantitative Aptitude - MCQ Practice Questions

Relative speed = 90 + 54 = 144 km/h = 40 m/s. Distance = 40 × 8 = 320m = sum of lengths.

Combined rate = $\frac{1}{4}$ + $\frac{1}{6}$ + $\frac{1}{12}$ = $\frac{3}{12}$ + $\frac{2}{12}$ + $\frac{1}{12}$ = $\frac{6}{12}$ = $\frac{1}{2}$. Time = 2 hours.

Let original = 100. After 30% increase = 130. After 30% decrease = 130 × 0.7 = 91. Net = 9% decrease.

Y's rate = $\frac{1}{18}$ - $\frac{1}{30}$ = $\frac{5}{90}$ - $\frac{3}{90}$ = $\frac{2}{90}$ = $\frac{1}{45}$. Y can complete in 45 days

Amount = 1000(1 + $\frac{10}{100}$)² = 1000 × 1.1 × 1.1 = Rs. 1210

Upstream speed = $\frac{30}{6}$ = 5 km/h. Downstream speed = $\frac{30}{3}$ = 10 km/h. Boat speed = (5+10)/2 = 7.5 km/h

Let original price = 100. After 25% increase = 125. After 20% decrease = 125 × $\frac{80}{100}$ = 100. Net = +5% gain

Combined rate = $\frac{1}{6}$ + $\frac{1}{8}$ + $\frac{1}{12}$ = $\frac{4}{24}$ + $\frac{3}{24}$ + $\frac{2}{24}$ = $\frac{9}{24}$

When two trains move towards each other, their relative speed is the sum of their individual speeds, and the total distance to cross is the sum of their lengths.

Step 1: Calculate total distance to be covered

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

Step 2: Convert relative speed from m/s to km/h context

The trains cross in 9 seconds, so the relative speed is:

Converting to km/h:

Step 3: Apply the relative speed formula for trains moving towards each other

When two trains move towards each other:

where $v_1=40\text{km/h}$ (first train) and $v_2$ is unknown.

Step 4: Solve for the second train's speed

**Answer: The speed of the second train is $120\text{km/h}$ (Option A)**

CP = 1200 × $\frac{100}{120}$ = Rs. 1000

Net rate = $\frac{1}{15}$ - $\frac{1}{20}$ = $\frac{4}{60}$ - $\frac{3}{60}$ = $\frac{1}{60}$. Time = 60 hours

Profit = 520 - 400 = 120. Profit% = ($\frac{120}{400}$) × 100 = 30%

Combined rate = $\frac{1}{10}$ + $\frac{1}{12}$ + $\frac{1}{15}$ = $\frac{6}{60}$ + $\frac{5}{60}$ + $\frac{4}{60}$ = $\frac{15}{60}$ = $\frac{1}{4}$. Time = 4 days

A = P(1 + r/100)^n = 8000(1 + $\frac{10}{100}$)^2 = 8000(1.1)^2 = 8000 × 1.21 = Rs. 9680

Let CP = 100. MP = 140. After 10% discount: SP = 140 × 0.9 = 126. Profit% = (126-100)/100 × 100 = 26%

A's efficiency = $\frac{1}{16}$ per day. B's efficiency = 1.6 × ($\frac{1}{16}$) = 1.$\frac{6}{16}$ = 0.1 = $\frac{1}{10}$. B takes 10 days

Let CP = x. SP = 1.25x. New CP = 0.8x, New SP = 1.25x - 90. Given: (1.25x - 90)/(0.8x) = 1.4. Solving: 1.25x - 90 = 1.12x, 0.13x = 90, x = 500.

A+B = $\frac{1}{12}$, B+C = $\frac{1}{15}$, A+C = $\frac{1}{20}$. Adding all: 2(A+B+C) = $\frac{1}{12}$ + $\frac{1}{15}$ + $\frac{1}{20}$ = $\frac{12}{60}$ = $\frac{1}{5}$. So A+B+C = $\frac{1}{10}$. Therefore A = $\frac{1}{10}$ - $\frac{1}{15}$ = $\frac{1}{30}$. A alone takes 30 days.

When two objects travel towards each other, their combined distance equals the sum of distances covered by each object individually.

Step 1: Find the Speed of the Slower Train

The slower train covers 240 km in 4 hours, so we can calculate its speed directly.

Step 2: Find the Speed of the Faster Train Using the Ratio

The ratio of speeds is 3:4, where 3 represents the slower train and 4 represents the faster train.

Step 3: Calculate Total Distance Between Stations

When trains travel towards each other and meet, the sum of distances covered by both equals the total distance between stations.

The distance between the two stations is 560 km.

The ratio of speeds of the two trains is:

3:4

Let their speeds be:

3x km/h and 4x km/h

The slower train travels at 3x km/h and covers 240 km in 4 hours.

So,

3x×4=240

12x=240

x=20

Thus,

Slower train speed =3x=60 km/h

Faster train speed =4x=80 km/h

In 4 hours, the faster train covers:

80×4=320 km

Total distance between the stations:

240+320=560 km

Therefore, the distance between the two stations is:

560 km

​

The answer is (A) 560 km.

Rate of pipe 1 = $\frac{1}{15}$, Rate of pipe 2 = $\frac{1}{20}$. Combined rate = $\frac{1}{15}$ + $\frac{1}{20}$ = $\frac{4}{60}$ + $\frac{3}{60}$ = $\frac{7}{60}$. Time = $\frac{60}{7}$ ≈ 8.57 minutes.