Quantitative Aptitude (Level Easy)

When two objects move in the same direction, their relative speed is the difference of their speeds. Here, relative speed = 50 - 32 = 18 kmph = 5 m/s. In 15 seconds, the faster train covers length = relative speed × time = 5 × 15 = 75m. This is the length needed for the faster train to completely pass the observer.

Each mesh occupies 8mm × 5mm = 40 square mm. One square meter = 1000mm × 1000mm = 1,000,000 square mm. Number of meshes = 1,000,000 ÷ 40 = 25,000. Ensure you convert square meters to square millimeters correctly.

If the amount triples in 3 years with annual compounding, then (1+r)³ = 3. To become 9 times, we need (1+r)ⁿ = 9. Since 9 = 3², we have (1+r)ⁿ = (1+r)⁶, giving n = 6 years. The doubling of the exponent (from 3 to 6) reflects the squaring relationship.

x% of y = (x/100) × y = (x × y)/100. Similarly, y% of x = (y/100) × x = (x × y)/100. Since multiplication is commutative, these are equal. The algebraic structure is symmetric, making x the correct answer.

Let original price = P and consumption = C. New price = 1.2P. For expenditure to remain same: P × C = 1.2P × C' where C' is new consumption. This gives C' = C/1.2 = (5/6)C. Reduction = C - C' = C - (5/6)C = C/6 = 16.66%. Alternatively, use the formula: reduction% = (100 × increase%) / (100 + increase%).

Let salary = S. Expenditure: household = S/2, rent = S/4, travel = S/5. Total expenditure = S/2 + S/4 + S/5 = (10S + 5S + 4S)/20 = 19S/20. Remaining = S - 19S/20 = S/20 = 50, giving S = 1000. The key is finding a common denominator and recognizing what fraction remains.

Total work = 15 × 21 × 8 = 2520 man-hours. Since 3 women = 2 men, 21 women = 14 men. Let required days = d. Then 14 × d × 6 = 2520, giving 84d = 2520, so d = 30 days. Convert women's capacity to equivalent men using the given ratio.

2880 = 2⁶ × 3² × 5¹. For a perfect square, all exponents must be even. 5 has exponent 1 (odd), so we must divide by 5 to get 2⁶ × 3² = 576 = 24². Dividing by 3 would give 960 = 2⁶ × 3¹ × 5¹, still not a perfect square due to odd exponents.

The cylinder volume is π × r² × h = π × 3² × 6 = 54π cubic cm. If spheres of diameter 3cm (radius 1.5cm) are made, each sphere has volume (4/3)π × 1.5³ = 4.5π. The number of spheres is 54π / 4.5π = 12, which is valid. Alternatively, if the question means the cylinder is recast into spheres of the same diameter as the cylinder's height, then diameter = 3cm.

5 men = 8 women, so 1 man = 8/5 woman. 3 men + 5 women = 3(8/5) + 5 = 49/5 woman-equivalent. Work done = 10 × 49/5 = 98 woman-days. To finish in 14 days: 98/14 = 7 women.

Let c be correct answers. Total marks = 4c - 2(150-c) = 480. Solving: 4c - 300 + 2c = 480 → 6c = 780 → c = 130. 130 correct × 4 = 520, 20 wrong × (-2) = -40, net = 480.

Let age of the son be x years.
Age of the father = x + 30 years
According to the question,
3(x + 5) = x + 30 + 5
3x + 15 = x+ 35 = 2x = 20
x = 10 years

Father's present age = 10 + 30 = 40 years

Simple Interest = P × R × T. 200 = 5000 × R × (6/12). Solving: 200 = 2500R → R = 200/2500 = 0.08 = 8% annually.

Let B take x days. A takes x-60 days. A works 3 times as fast, so x/(x-60) = 3. Solving: x = 3x - 180 → 2x = 180 → x = 90 (B's days), A = 30 days. Together: 1/30 + 1/90 = 4/90, so time = 90/4 = 22.5 days.

8192 + 192 + 3 = 8387. Converting to binary: 8192 (2^13) + 128 + 64 + 2 + 1. Binary: 10000011000011. Counting 1s: 4.

Starting at Rs.2, to reach Rs.5 means gaining Rs.3 net. Since wins = +1 and losses = -1, we need 3 more wins than losses. With max 5 losses, valid (wins, losses): (3,0), (4,1), (5,2), (6,3), (7,4), (8,5). Count paths: 1 + 4 + 10 + 20 + 35 + 56 = 126 combinations... wait. Actually, this is a lattice path problem. From (0,0) to (5,3) where x=losses, y=wins-y. Total ways = C(8,3) = 56. But this doesn't match 16. Re-reading: the constraint is 'can lose only 5 times' and 'out if earns Rs.5'. Shortest path: need +3 net with max 5 losses. If we take exactly 5 losses, need 8 wins. Number of sequences ending at exactly +3 before hitting +5 or -5... actually the answer 16 likely comes from a specific interpretation of the path constraints.

Given x/y = 4, x = 4y. We want (2x-y)/x as percentage. Substituting: (8y-y)/(4y) = 7y/4y = 7/4 = 1.75 = 175%.

If A says 'I am a liar', this creates a logical paradox. If A is truthful, he cannot truthfully say he's a liar. If A is lying, then the statement 'I am a liar' is false, meaning he's truthful - contradiction. Therefore A cannot consistently make this statement. B claims 'A says that he is a liar' - since A cannot consistently say this, B must be lying.

Total pixels = 1024 × 1280 = 1,310,720. Each pixel needs 16 million colors = 2^24 colors = 24 bits per pixel. Total bits = 1,310,720 × 24 = 31,457,280 bits. Converting to bytes: /8 = 3,932,160 bytes. Converting to MB: /1024² = 3.75 MB ≈ 4MB.

When discounts are applied successively, the second discount applies to the reduced amount, not the original. After 20% discount, you pay 80% of original. Then 15% off that means you pay 85% of 80%, which is 68% of original. So total discount is 32%, not 35% (which would be simple addition of 20+15).

At 8:30, the hour hand is halfway between 8 and 9 (at 255 degrees from 12), and the minute hand is at 6 (180 degrees from 12). The angle between them is 255-180=75 degrees. This is because the hour hand moves 30 degrees per hour plus 0.5 degrees per minute.

The tank holds g liters when full. If a liters are removed, the fraction removed is a/g. Option A (g-a) is what remains, not what was removed. Option B is a division that doesn't represent a fraction. Option C correctly shows the fraction as a/g.

We need b as fraction of d, so express b in terms of d. Given: b=2c/3, and c=2d/3, so b=2(2d/3)/3=4d/9. Therefore b is 4/9 of d. The key is substituting step by step until you reach the target variable.