Mathematics

A's daily work = 1/(12*8) = 1/96 of the work; B's daily work = 1/(8*10) = 1/80 of the work. Together working 8 hours a day, combined daily work = 8*(1/96 + 1/80) = 8*(5/480 + 6/480) = 8*(11/480) = 11/60. Total days = 1 / (11/60) = 60/11 = 5 5/11 days. However, since they work 8 hours a day, the total days = 60/11 ≈ 5.45 days, which matches option A. Rechecking calculations shows option A is correct, so correct_answer is A.

Pipes X and Y fill the tank at rates of 1/15 and 1/20 per hour respectively, and pipe Z empties the tank at 1/25 per hour. When all three pipes are open, the net fill rate is 1/15 + 1/20 - 1/25 = 23/300 tank per hour. After 10 hours, the tank is filled by 10 * 23/300 = 23/30. The remaining part of the tank to be filled is 1 - 23/30 = 7/30. After closing pipe Z, pipes X and Y fill at a combined rate of 1/15 + 1/20 = 7/60 tank per hour. The time to fill the remaining 7/30 of the tank is (7/30) / (7/60) = 2 hours. Therefore, the total time to fill the tank is 10 + 2 = 12 hours. Hence, the correct answer is 12 hours, option A.

P can complete 1/18 of the work per day, and Q can complete 1/15 of the work per day. Q worked for 10 days, so Q completed 10/15 = 2/3 of the work. The remaining work is 1 - 2/3 = 1/3. P needs to complete this remaining 1/3 of the work. Since P completes 1/18 of the work per day, the number of days P needs is (1/3) / (1/18) = (1/3) * 18 = 6 days. Therefore, the correct answer is B, 6 days.

If the three adjacent faces of a rectangular box have areas A = xy, B = yz, and C = zx, where x, y, and z are the edges meeting at a point, then the product ABC = (xy)(yz)(zx) = (xyz)^2, which is the square of the volume of the box.

The tap fills the tank at a rate of 1/32 per minute, and the other empties it at 1/16 per minute. The net rate when both taps are open is (1/32) - (1/16) = -1/32 tank per minute, meaning the tank is emptying at a rate of 1/32 of the tank per minute. Since the tank is initially half full, it will take (1/2) ÷ (1/32) = 16 minutes to empty the tank completely. Therefore, the correct answer is 16 minutes, option C.

Mansoor-Ul-Haque types at a rate of 32 pages / 6 hours = 16/3 pages per hour. Aaqib types at a rate of 40 pages / 5 hours = 8 pages per hour. Together, their combined rate is (16/3) + 8 = (16/3) + (24/3) = 40/3 pages per hour. To type 110 pages, time needed = 110 / (40/3) = 110 * (3/40) = 8.25 hours, which is 8 hours 15 minutes. However, this contradicts the initial correct answer C. Rechecking calculations: Mansoor-Ul-Haque rate = 32/6 ≈ 5.33 pages/hour, Aaqib rate = 40/5 = 8 pages/hour, combined rate = 5.33 + 8 = 13.33 pages/hour. Time = 110 / 13.33 ≈ 8.25 hours = 8 hours 15 minutes. So the original correct answer C (8 hour 15 minutes) is correct. Therefore, the initial calculation was incorrect. The correct answer is C.

Since Kamal completes the work in 20 days, his work rate is 1/20 of the work per day. Suresh is 25% more efficient than Kamal, meaning Suresh's work rate is 1.25 times Kamal's rate. Therefore, Suresh's work rate = 1.25 × (1/20) = 1/16 of the work per day. Hence, Suresh will complete the work in 16 days (1 ÷ (1/16) = 16).

Jameel works from 9:00 am to 2:00 pm, which is 5 hours. His work rate is 1/15 of the task per hour, so in 5 hours he completes 5/15 = 1/3 of the task. The remaining task is 2/3. Nasir starts working at 4:00 pm after a 2-hour break. Nasir's work rate is 1/12 of the task per hour. To complete the remaining 2/3 of the task, Nasir needs (2/3) / (1/12) = 8 hours. Starting at 4:00 pm and working for 8 hours means the task finishes at 12:00 am (midnight). Therefore, the correct answer is C (12:00 am).

Given the edges of the cuboid are in the ratio 1:2:3, let the edges be x, 2x, and 3x. The surface area is 2(x*2x + 2x*3x + 3x*x) = 2(2x^2 + 6x^2 + 3x^2) = 2(11x^2) = 22x^2. Given surface area = 88 cm², so 22x² = 88, hence x² = 4 and x = 2. The volume = x * 2x * 3x = 6x³ = 6 * 8 = 48 cm³. However, this contradicts the calculation; rechecking: volume = x * 2x * 3x = 6x³ = 6 * (2)³ = 6 * 8 = 48 cm³. So the volume is 48 cm³, which matches option B. The initial explanation was incorrect; the correct volume is 48 cm³, so the correct answer is B.

The two taps fill the cistern at rates of 1/12 and 1/15 cisterns per minute, respectively. Combined, they fill at (1/12 + 1/15) = 9/60 = 3/20 cisterns per minute. When the outlet pipe is also open, the cistern fills in 20 minutes, so the net filling rate is 1/20 cisterns per minute. Let the outlet pipe's emptying rate be 1/x. Then, (3/20) - (1/x) = 1/20, solving gives x = 40 minutes.

First, calculate total bull-hours needed to plough 20 fields: 10 bulls × 3 days × 10 hours = 300 bull-hours. So, 1 field requires 300/20 = 15 bull-hours. For 32 fields, total bull-hours = 32 × 15 = 480. With 30 bulls working 8 hours a day, daily bull-hours = 30 × 8 = 240. Days required = 480 / 240 = 2 days. However, this conflicts with the options, so rechecking: 10 bulls × 3 days × 10 hours = 300 bull-hours for 20 fields, so 1 field = 15 bull-hours. For 32 fields, total bull-hours = 480. With 30 bulls × 8 hours = 240 bull-hours/day, days = 480/240 = 2 days. Option A is 2, so correct answer is A, not B. Correction made accordingly.

The total work can be considered as 28 men × 15 days = 420 man-days. Since the amount of work is constant, the time taken is inversely proportional to the number of men. Therefore, if 21 men are working, the time taken will be 420 man-days ÷ 21 men = 20 days. Hence, the correct answer is 20 days, which corresponds to option D.

Given the problem: P, Q, and R together earn Rs.1620 in 9 days, so their combined daily earning is Rs.1620/9 = Rs.180 per day. P and R together earn Rs.600 in 5 days, so their combined daily earning is Rs.600/5 = Rs.120 per day. Q and R together earn Rs.910 in 7 days, so their combined daily earning is Rs.910/7 = Rs.130 per day. From these, we have three equations: 1) p + q + r = 180 2) p + r = 120 3) q + r = 130 Subtracting equation (2) from (1) gives q = 60. Subtracting equation (3) from (1) gives p = 50. Using p + r = 120 and p = 50, we get r = 70. Therefore, R earns Rs.70 per day, which corresponds to option B.

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.

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 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.

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 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.

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 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).

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 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 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.

A and B together complete 1/15 of the work per day, and B alone completes 1/20 per day. Therefore, A's work rate is 1/15 - 1/20 = 1/60 per day, so A alone can do the work in 60 days.

Let the distance travelled on foot be x km. Then the distance travelled by bicycle is (61 - x) km. The time taken on foot is x/4 hours, and the time on bicycle is (61 - x)/9 hours. The total time is 9 hours, so x/4 + (61 - x)/9 = 9. Solving this equation gives x = 16 km, which matches option C.