Mathematics

Let the length of the journey be x km and the scheduled time be t hours. At 40 kmph, time taken is t = x/40. At 35 kmph, time taken is x/35, which is 15 minutes (0.25 hours) more than t. So, x/35 - x/40 = 0.25. Solving gives x = 70 km.

Since A is thrice as efficient as B, A takes one-third the time B takes. Given A takes 10 days less than B, let B's time be x days. Then A's time is x - 10 days, and A's time is also x/3. So, x - 10 = x/3, solving gives x = 15 days. However, this contradicts the options. Rechecking: x - 10 = x/3 implies 3x - 30 = x, so 2x = 30, x = 15 days. So B takes 15 days, which corresponds to option A. Therefore, the original correct answer A (15 days) is correct. The initial confusion was in explanation wording. The correct answer is A.

Bilal completes 1/15 of the work per day, and Jalal completes 1/12 per day. Together, they complete 1/15 + 1/12 = 4/60 + 5/60 = 9/60 = 3/20 of the work per day. In 4 days, they complete 4 × 3/20 = 12/20 = 3/5 of the work. The fraction left is 1 - 3/5 = 2/5. Therefore, the fraction of the work left after 4 days is 2/5, which corresponds to option C.

A's work rate is 1/30 per day and B's work rate is 1/40 per day. Together, their combined rate is 1/30 + 1/40 = (4/120) + (3/120) = 7/120 work per day. Therefore, they can complete the work in 120/7 days.

The train travels 600 km at an average speed of 100 km/h, so the running time without stops is 600 ÷ 100 = 6 hours. The train stops for 3 minutes after every 75 km. Since 600 km ÷ 75 km = 8 segments, there are 7 stops (one after each segment except the last). Total stopping time is 7 × 3 = 21 minutes. Therefore, total time = 6 hours + 21 minutes = 6 hours 21 minutes, which corresponds to option A.

First, find the total man-hours for 6 men working 4 hours: 6 × 4 = 24 man-hours to complete 50 tasks. So, 1 task requires 24/50 = 0.48 man-hours. For 10 men working 6 hours, total man-hours = 10 × 6 = 60. Number of tasks = 60 / 0.48 = 125 tasks.

The leak empties the tank in 9 hours, so leak rate = tank capacity / 9. The inlet fills at 10 liters/min = 600 liters/hour. When both operate, tank empties in 16 hours, so net rate = tank capacity / 16 (emptying). Setting net rate = leak rate - inlet rate, we solve for tank capacity and get approximately 12,444 liters.

The efficiency ratio of Rashid and Danish is given as 5:8. Efficiency is inversely proportional to the time taken to complete the work. Therefore, the time taken ratio is the inverse, i.e., 8:5. Let the time taken by Rashid be 8x days and by Danish be 5x days. Given that Danish takes 51 days less than Rashid, we have 8x - 5x = 3x = 51 days, which gives x = 17. Hence, Rashid's time to complete the work is 8 * 17 = 136 days. This matches option D, confirming it as the correct answer.

Let the total work be 1 unit. Since R alone takes 50 days, R's work rate is 1/50 per day. P can do the work in the same time as Q and R together, so P's rate = Q's rate + R's rate. Given P and Q together take 10 days, their combined rate is 1/10 per day. Using these relations, we find Q's rate = 1/30 per day, so Q alone can do the work in 30 days.

Given the radius r is half the height h, let h = 2r. The curved surface area (CSA) is given as 616 sq. cm. The formula for CSA of a cylinder is 2πrh. Substituting h = 2r, we get 2πr(2r) = 4πr² = 616. Using π = 22/7, 4 × (22/7) × r² = 616, which simplifies to r² = 49, so r = 7 cm and h = 14 cm. The volume V = πr²h = (22/7) × 49 × 14 = 2156 cm³ = 2.156 liters. Among the options, 1.9 liters (D) is the closest approximation to the actual volume.