Mathematics

Let the total distance be x km. The man travels half the distance (x/2) at 21 km/hr and the other half (x/2) at 24 km/hr. Total time = (x/2)/21 + (x/2)/24 = 10 hours. Solving for x gives x = 112 km.

Let the two numbers be 2x and 3x. Their cubes sum to 280: (2x)^3 + (3x)^3 = 8x^3 + 27x^3 = 35x^3 = 280. Solving for x^3 gives x^3 = 280 / 35 = 8, so x = 2. The two numbers are 2x = 4 and 3x = 6. The smallest number is 4, which corresponds to option A.

To find the speed in km/h, convert the distance and time to compatible units. Distance = 600 meters = 0.6 kilometers. Time = 5 minutes = 5/60 hours = 1/12 hours. Speed = distance/time = 0.6 km / (1/12) hours = 0.6 * 12 = 7.2 km/h. Therefore, the correct answer is option D (7.2 km/h).

Nasir's investment is Rs.3000 for 6 months, so his capital-time product is 3000 × 6 = 18000. Changaz's investment is Rs.6000 for 12 months, so 6000 × 12 = 72000. The ratio of their investments is 72000:18000 = 4:1. Total profit Rs.240 is divided in this ratio, so Nasir's share = (1/5) × 240 = Rs.48. However, the calculation shows Rs.48, which corresponds to option D, so the original answer D is correct. Rechecking the calculation: Nasir's share = (3000×6)/(6000×12 + 3000×6) × 240 = 18000/90000 × 240 = 1/5 × 240 = 48. Therefore, the correct answer is D = 48. The original answer D is correct; the explanation was missing and is now provided. Difficulty is easy based on the straightforward calculation.

To divide Rs.2000 in the ratio 3:2, first find the total parts: 3 + 2 = 5. Each part is Rs.2000 ÷ 5 = Rs.400. Therefore, the shares are 3 parts = Rs.1200 and 2 parts = Rs.800, matching option A.

Let the number be x. According to the problem, 40% of x is 190 more than 20% of 650. So, 0.4x = 0.2*650 + 190. Calculating 0.2*650 = 130, so 0.4x = 130 + 190 = 320. Therefore, x = 320 / 0.4 = 800. Hence, the correct answer is 800.

The boatman's speed in still water is 7 km/hr and the river speed is 3 km/hr. Upstream speed = 7 - 3 = 4 km/hr, downstream speed = 7 + 3 = 10 km/hr. Let the distance be d km. Time difference is 6 hours: d/4 - d/10 = 6. Solving gives d = 40 km.

The scale 1:500 means 1 cm on the plan represents 500 cm (or 5 m) in actual length. The actual length is 30 cm × 5 m/cm = 150 m, and the actual breadth is 20 cm × 5 m/cm = 100 m. Therefore, the actual area = 150 m × 100 m = 15,000 m², which corresponds to option D.

The problem involves three numbers with given ratios and a total sum. The first and second numbers are in the ratio 8:11, so let them be 8k and 11k. The second and third numbers are in the ratio 5:7, so let them be 5m and 7m. Since the second number is common, 11k = 5m, which gives m = 11k/5. The third number is then 7m = 7*(11k/5) = 77k/5. The sum of the three numbers is 8k + 11k + 77k/5 = (40k/5) + (55k/5) + (77k/5) = 172k/5. Given the sum is 172, we have 172k/5 = 172, so k = 5. The second number is 11k = 11*5 = 55. Therefore, the correct answer is B (55).

The ratio of boys to girls is 7:8, so total parts = 7 + 8 = 15. Number of boys = (7/15) × 90 = 42.