Mathematics

Yalmaz's speed = 400 m / 120 s = 10/3 m/s. Rayan's speed = 1000 m / 300 s = 10/3 m/s. Both speeds are equal, so the ratio is 1:1. However, checking the calculations carefully: Yalmaz's speed = 400/120 = 3.33 m/s, Rayan's speed = 1000/300 = 3.33 m/s, so the ratio is indeed 1:1. The original correct answer was D (1:1), which is correct. The options are correct, but option B (4:3) is incorrect. Therefore, the correct answer remains D.

The equation given is x + x² = 182, which can be rewritten as x² + x - 182 = 0. Factoring this quadratic gives (x + 14)(x - 13) = 0, so the solutions are x = 13 and x = -14. Among the options provided, 13 is the correct positive solution, which corresponds to option D.

Given that x varies directly as 4y - 1, we write x = k(4y - 1). Using the point (y=2, x=14), we find k: 14 = k(4*2 - 1) = k(8 - 1) = 7k, so k = 2. Then, for y=5, x = 2(4*5 - 1) = 2(20 - 1) = 2*19 = 38. However, 38 is option A, so the correct answer is A, not B. Rechecking calculations: 14 = k(7) => k=2, x=2(19)=38, which matches option A. Therefore, the original correct_answer 'A' is correct. The explanation was missing and is now provided. Difficulty is medium due to algebraic manipulation.

The train's speed is 60 km/hr, which converts to 16.67 m/s (60 × 1000 / 3600 or 60 × 5/18). The time to pass a pole equals the length of the train divided by its speed: 125 m / 16.67 m/s ≈ 7.5 seconds. Therefore, the correct answer is option C (7.5s).

The money is divided in the ratio 7:4:3:2 among A, B, C, and D respectively. Let the common multiplier be x. Then A's share = 7x and D's share = 2x. Given that D gets Rs. 500 less than A, we have 7x - 2x = 500, which simplifies to 5x = 500, so x = 100. The total amount is the sum of all shares: (7 + 4 + 3 + 2) x = 16 x 100 = Rs. 1600. Therefore, the correct total amount is Rs. 1600, which corresponds to option C.

Let the three numbers be x, y, and z. Given x : y = 2 : 3, so x = (2/3)y. Also, y : z = 5 : 8, so z = (8/5)y. The sum is x + y + z = 98, substituting gives (2/3)y + y + (8/5)y = 98. Finding a common denominator and solving for y yields y = 30.

Let the number of 50 paise, 1 rupee, and 2 rupee coins be 2x, 5x, and 8x respectively. The total amount is (0.5)(2x) + (1)(5x) + (2)(8x) = x + 5x + 16x = 22x rupees. Given total amount is Rs. 352, so 22x = 352, x = 16. Total coins = 2x + 5x + 8x = 15x = 15*16 = 240.

The average speed is calculated by dividing the total distance by the total time. Total distance = 160 + 160 = 320 km. Time for first part = 160/64 = 2.5 hours; time for second part = 160/80 = 2 hours. Total time = 4.5 hours. Average speed = 320/4.5 ≈ 71.11 km/hr, which corresponds to option C. However, the calculation shows 71.11 km/hr, so option C is correct. The original correct_answer was C, but option D is 72.21 km/hr which is incorrect. Therefore, the original correct_answer C is correct, but option B has a typo with an extra space. The explanation was missing and is now added. Difficulty is medium because it requires calculation of average speed over different speeds.

Let the usual time be T. Walking at 5/6 speed means time taken is T × (6/5) = 1.2T. The delay is 40 minutes, so 1.2T - T = 40 minutes ⇒ 0.2T = 40 ⇒ T = 200 minutes = 3 hours 20 minutes. Hence, option A is correct.

Given x% of 200 equals y% of 250, we have (x/100)*200 = (y/100)*250, which simplifies to 2x = 2.5y or 4x = 5y. Therefore, y:x = 4:5, matching option D.