Mathematics

80% of 40 is calculated as 0.8 × 40 = 32. 4/5 of 25 is calculated as (4/5) × 25 = 20. The difference between these two values is 32 - 20 = 12. Therefore, 80% of 40 is greater than 4/5 of 25 by 12, which corresponds to option D.

Let the distance travelled by car be x km and by train be y km. Given y = x + 150 and x + y = 750. Substituting y, we get x + (x + 150) = 750, so 2x = 600, x = 300. Then y = 450. The ratio x:y = 300:450 = 2:3. However, the question asks for x:y, which is car to train, so the ratio is 2:3. The correct answer is A, not B.

The car passes A and B in 9 and 10 seconds respectively. Using relative speed, for A: relative speed = car speed - 6 km/hr; for B: relative speed = car speed - 12 km/hr. Since the distance passed (the length of the car) is equal in both cases, we can set up the equation: (car speed - 6) * 9 = (car speed - 12) * 10. Expanding this gives 9 * car speed - 54 = 10 * car speed - 120. Solving for the car's speed gives 120 - 54 = 66 km/hr.

Let the speed of the car be x kmph. Then the speed of the train is 1.5x kmph. Both cover 75 km in the same total time, but the train loses 12.5 minutes (which is 12.5/60 = 0.2083 hours) due to stops. So, time taken by car = 75/x hours. Time taken by train = 75/(1.5x) + 0.2083 hours. Since they arrive simultaneously, 75/x = 75/(1.5x) + 0.2083. Solving this gives x = 80 kmph.

The original seats are in the ratio 5:7:8. Increasing them by 40%, 50%, and 75% respectively results in new seat counts proportional to 5×1.4=7, 7×1.5=10.5, and 8×1.75=14. The ratio 7:10.5:14 simplifies to 2:3:4. However, this matches option A, so option A is correct, not 'None of these'. Therefore, the correct answer is A.

The mean proportion between two numbers a and b is given by the square root of their product, √(a×b). Here, √(5×45) = √225 = 15, which corresponds to option B.

Let the number of 1 rupee, 2 rupee, and 5 rupee coins be 3x, 5x, and 4x respectively. The total amount is calculated as 1*3x + 2*5x + 5*4x = 3x + 10x + 20x = 33x. Given the total amount is Rs. 264, we have 33x = 264, which gives x = 8. Therefore, the number of 1 rupee coins is 3x = 3*8 = 24. Hence, the correct answer is option C (24).

Given that x is 20% more than z, we have x = 1.20z. Similarly, y is 80% more than z, so y = 1.80z. The ratio x:y = 1.20z : 1.80z = 1.20 : 1.80. Simplifying this ratio by dividing both terms by 0.60 gives 2 : 3. Therefore, the correct ratio x:y is 2:3, which corresponds to option D.

Let the time taken to walk one way be W hours and to ride one way be R hours. Given that walking one way and riding back takes 5 hours 45 minutes (5.75 hours), so W + R = 5.75. Riding both ways would save 2 hours compared to walking one way and riding back, so 2R = 5.75 - 2 = 3.75 hours, thus R = 1.875 hours. From W + R = 5.75, W = 3.875 hours. Therefore, walking both ways takes 2W = 7.75 hours or 7 hours 45 minutes. However, the question states he would have gained 2 hours by riding both ways compared to walking and riding, so the total walking both ways time is 5.75 + 2 = 7.75 hours, which matches option C (7 hrs 45 min). But the question asks for the time to walk both ways, which is 2W = 2 × 3.875 = 7.75 hours or 7 hrs 45 min, so option C is correct. The initial calculation was incorrect; the correct answer is C.

Since the total costs are the same, the area ratio is inversely proportional to the cost per sq. ft. Therefore, area ratio = cost per sq. ft of commercial space : cost per sq. ft of flat = 9500 : 4500 = 19 : 9. So, the ratio of their areas is 9:19 (flat : commercial space).