Mathematics

The rates of pipes P, Q, and R are 1/20, 1/15, and 1/12 cisterns per minute respectively. Adding these rates gives (1/20 + 1/15 + 1/12) = (3/60 + 4/60 + 5/60) = 12/60 = 1/5 cistern per minute. Therefore, together they fill the cistern in 5 minutes. This matches option A, confirming that the correct answer is 5 minutes.

The average speed for the entire trip is calculated by dividing the total distance by the total time taken. The man travels 10 km at 12 km/h, taking 10/12 ≈ 0.833 hours, and then 12 km at 10 km/h, taking 12/10 = 1.2 hours. Total distance = 10 + 12 = 22 km. Total time = 0.833 + 1.2 = 2.033 hours. Average speed = total distance / total time = 22 / 2.033 ≈ 10.82 km/h, which rounds to approximately 10.8 km/h. Therefore, the correct answer is option D (10.8 kmph), not A (11.2 kmph).

The two trains approach each other at a combined speed of 70 + 50 = 120 mph. They start 120 miles apart, so they collide after 120 / 120 = 1 hour. The bird flies continuously at 85 mph for that 1 hour, so it covers 85 miles.

The diagonal (d) of a cube with side length s is given by the formula d = s√3. Given the diagonal is 4√3 cm, we solve for s: s√3 = 4√3, so s = 4 cm. The volume of the cube is s³ = 4³ = 64 cubic cm. Therefore, the correct answer is D (64).

If 10 workers make 10 tables in 10 days, then 1 worker makes 1 table in 10 days. Therefore, 5 workers making 5 tables will also take 10 days.

The original speed is 10 km in 12 minutes, which is 50 km/h. Decreasing the speed by 5 km/h gives 45 km/h. Time = Distance / Speed = 10 km / 45 km/h = 4/18 hours = 13 min 20 sec, which matches option D.

Let the work done by one man in one day be M and one woman be W. From the first scenario: 6M + 8W = 1/10 (work per day). From the second: 26M + 48W = 1/2. Solving these equations gives the daily work rates for men and women. Using these, 15M + 20W = ? The calculation shows they complete the work in 6 days.

The average speed for a round trip where the distances are equal but speeds differ is given by the formula: Average speed = 2 * (speed1 * speed2) / (speed1 + speed2). Here, speed1 = 30 kmph and speed2 = 60 kmph. Plugging in the values, Average speed = 2 * (30 * 60) / (30 + 60) = 3600 / 90 = 40 kmph. This matches option D, so the correct answer is D.

The total distance covered is calculated by summing the distances covered in each segment of the journey. For the first 2 hours at 120 km/h, the distance is 120 × 2 = 240 km. For the next half an hour (0.5 hours) at 100 km/h, the distance is 100 × 0.5 = 50 km. Adding these gives a total distance of 240 + 50 = 290 km. Therefore, the correct answer is option B (290 km).

The total capacity of the tank is 12 buckets × 13.5 litres = 162 litres. To find how many 9-litre buckets are needed, divide 162 litres by 9 litres per bucket, which equals 18 buckets.