Quantitative Aptitude - MCQ Practice Questions

To solve percentage problems, we first find the original number, then calculate the required percentage of it.

Step 1: Find the Original Number

Since 25% of the number equals 80, we set up an equation where the unknown number is x.

Step 2: Calculate 60% of That Number

Now that we know the original number is 320, we find 60% of it.

The answer is (A) 192

Discount = 30% of 1000 = 300. Selling price = 1000 - 300 = Rs. 700

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

Tank capacities: 2x, 3x, 4x. Filling rates: 2x/6, 3x/8, 4x/12 per hour. Time to fill: Tank1 = 6hrs, Tank2 = 8hrs, Tank3 = 12hrs. Tank1 fills first in 6 hours. But answer suggests C (Tank3). Rechecking: if pipes fill tanks with different capacities, Tank3 (capacity 4x) filled by pipe with rate 4x/12 takes 12 hours. Standard logic: smaller capacity fills first. Clarification needed in question. Marking A as logical answer.

Let original number = x. After 30% increase: 1.3x. After 20% decrease: 1.3x × 0.8 = 1.04x = 624. x = $\frac{624}{1}$.04 = 600

Let amount in scheme 1 = x. Amount in scheme 2 = 10000-x. Interest = (x×12×3)/100 + ((10000-x)×15×3)/100 = 4050. 36x + 450000 - 45x = 405000. -9x = -45000. x = 5000

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.

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.

When a number undergoes multiple percentage changes, we must apply each change sequentially to find the net effect.

Step 1: Apply the 40% Increase

Starting with an original number, a 40% increase multiplies it by 1.40.

Step 2: Apply the 30% Decrease

A 30% decrease means we retain 70% of the value, so we multiply by 0.70.

Step 3: Calculate Net Change

The final value is 0.98x, which is 98% of the original value x.

The net change is a 2% decrease. Answer: (B)

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.

SI = P × R × T / 100. 1200 = P × 8 × $\frac{3}{100}$. P = (1200 × 100) / 24 = 5000.

A = P(1 + R/100)^T = 12000(1.1)^2 = 12000 × 1.21 = 14,520.

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

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The answer is (A) 560 km.

Let CP = 100. MP = 160. After 25% discount, SP = 160 × 0.75 = 120. Profit = 120 - 100 = 20. Profit% = 20%.

x% of 400 = 20% of 500. (x/100) × 400 = 0.2 × 500. 4x = 100. x = 25.

B takes 30 days, so B's rate = $\frac{1}{30}$. A works twice as fast, so A's rate = $\frac{2}{30}$ = $\frac{1}{15}$. Combined rate = $\frac{1}{30}$ + $\frac{1}{15}$ = $\frac{1}{30}$ + $\frac{2}{30}$ = $\frac{3}{30}$ = $\frac{1}{10}$. Time taken = 10 days.