Mathematics

The car takes 30 seconds to reach the 16th pole, which means it covers 15 intervals (since the first pole is the start). The time per interval is 30/15 = 2 seconds. There are 20 intervals to reach the 21st pole, so total time is 20 * 2 = 40 seconds.

Let the first number be x and the second number be y. Given 40% of x equals two-thirds of y, so 0.4x = (2/3)y. Rearranging, x/y = (2/3) / 0.4 = (2/3) / (2/5) = (2/3) * (5/2) = 5/3. Thus, the ratio of the first number to the second number is 5:3.

Let the digits of the number be x and y. Original number = 10x + y and reversed number = 10y + x. Given 10y + x = 10x + y + 18 and x + y = 8. Simplifying gives y - x = 2. Solving with x + y = 8 gives x = 3 and y = 5, so the original number is 35.

Given X:Y = 2:3 and Y:Z = 4:5, we first equalize the Y terms by finding the least common multiple of 3 and 4, which is 12. Scaling X:Y to 8:12 and Y:Z to 12:15, we combine to get X:Y:Z = 8:12:15.

The sides of the triangle are in the ratio 4:3:2. Let the sides be 4x, 3x, and 2x. The perimeter is the sum of the sides: 4x + 3x + 2x = 9x. Given the perimeter is 81 cm, we have 9x = 81, so x = 9 cm. The largest side is 4x = 4 * 9 = 36 cm. Therefore, the correct answer is 36 cm, which corresponds to option C.

Let the number be x. 60% of x is 0.6x. According to the problem, 0.6x - 40 = 50. Adding 40 to both sides gives 0.6x = 90. Dividing both sides by 0.6 gives x = 150. However, 150 is option A, so we need to re-check the calculation. Actually, 0.6x - 40 = 50 implies 0.6x = 90, so x = 90 / 0.6 = 150. Therefore, the correct answer is A, not B. The initial correction was incorrect. The correct answer is A (150).

The distance covered is the same, so speed and time are inversely proportional. Original speed is 24 kmph for 50 minutes; to cover the same distance in 40 minutes, speed = (24 kmph × 50) / 40 = 30 kmph.

Using the allegation method, the difference between the cost of the second type and the mixture is 19 - 14.2 = 4.8, and the difference between the mixture and the first type is 14.2 - 13 = 1.2. The ratio of the quantities mixed is therefore 4.8 : 1.2, which simplifies to 4 : 1. This means the two types of rice are mixed in the ratio 4:1 (first type : second type) to get the mixture costing Rs. 14.2 per kg. This matches option B.

Let the two numbers be 5x and 9x. After decreasing each by 5, the ratio becomes (5x - 5) : (9x - 5) = 5 : 11. Solving the equation (5x - 5)/(9x - 5) = 5/11 gives x = 7. Therefore, the numbers are 5*7 = 35 and 9*7 = 63. However, none of the options match these numbers, so let's check the options by substituting back into the ratio condition. Option B (21, 37) gives (21 - 5) : (37 - 5) = 16 : 32 = 1 : 2, not 5 : 11. Option D (15, 27) gives (15 - 5) : (27 - 5) = 10 : 22 = 5 : 11, which matches the second ratio. But the original ratio 15 : 27 simplifies to 5 : 9, which matches the first ratio. Therefore, the correct answer is D (15, 27).

If a 3/4 full tank allows the car to travel 360 km, then a full tank would allow it to travel (360 km) ÷ (3/4) = 480 km. Therefore, with a 2/3 full tank, the car can travel 480 km × (2/3) = 320 km. However, since 320 km is option B, but the question asks how many km with 2/3 full tank, the correct answer is 320 km (option B). The original correct_answer was B, which matches this calculation, so the original answer is correct. The explanation was missing and has been added. Difficulty is set to easy based on the straightforward proportional calculation.