Mathematics

The problem states that Farjan and Kashif together complete the task in 30 days, so their combined work rate is 1/30 of the task per day. They work together for 20 days, completing 20/30 = 2/3 of the task. The remaining 1/3 of the task is completed by Kashif alone in 25 days, so Kashif's work rate is (1/3)/25 = 1/75 of the task per day. Farjan's work rate is the combined rate minus Kashif's rate: (1/30) - (1/75) = (5/150) - (2/150) = 3/150 = 1/50 of the task per day. Therefore, Farjan alone takes 50 days to complete the entire task. This matches option A, confirming that the correct answer is A (50).

The car covers 42 km in 1 hour 40 minutes 48 seconds at 5/7 of its actual speed. Converting the time to hours: 1 hr + 40/60 hr + 48/3600 hr = 1.68 hours. Speed at 5/7 actual speed = distance/time = 42/1.68 = 25 km/hr. Therefore, actual speed = (7/5) * 25 = 35 km/hr. However, this calculation shows 35 km/hr, matching option B. Rechecking: 1 hr 40 min 48 sec = 1 + 40/60 + 48/3600 = 1 + 0.6667 + 0.0133 = 1.68 hr. Speed = 42/1.68 = 25 km/hr (5/7 actual speed). Actual speed = (7/5)*25 = 35 km/hr. So the correct answer is B, not D. Explanation corrected accordingly.

The volume of the cylindrical tank is given as 246.4 litres, which converts to 0.2464 cubic meters (since 1 litre = 0.001 cubic meters). The height of the tank is 4 meters. Using the formula for the volume of a cylinder V = πr²h, we substitute the known values: 0.2464 = πr² × 4. Solving for r² gives r² = 0.2464 / (4π) ≈ 0.0196, so r ≈ 0.14 meters. The diameter is twice the radius, so diameter ≈ 0.28 meters. This matches option B. The explanation in the original question had confusing statements about decimal placement and incorrect mentions of 2.8 m, which are not relevant. The correct diameter is 0.28 m, which is option B.

C takes 6 days to complete half the work, so C's 1 day work = 1/12 of the work. In 4 days, C completes 4 × 1/12 = 1/3 of the work. The remaining work is 2/3. D takes 5 days to complete one-third of the work, so D's 1 day work = 1/15 of the work. To complete the remaining 2/3 of the work, D needs (2/3) ÷ (1/15) = (2/3) × 15 = 10 days. Therefore, D will complete the rest of the work in 10 days, which corresponds to option A.

First, find the total work in man-days for the first wall: 15 men × 30 days = 450 man-days to build 500 m. The work per meter is 450 man-days / 500 m = 0.9 man-days per meter. For a 1.2 km (1200 m) wall, total work = 1200 m × 0.9 man-days/m = 1080 man-days. With 30 men working, days required = 1080 man-days / 30 men = 36 days. However, this contradicts the initial calculation, so let's re-check: 15 men × 30 days = 450 man-days for 500 m, so 1 m requires 450/500 = 0.9 man-days. For 1200 m, total man-days = 1200 × 0.9 = 1080. With 30 men, days = 1080/30 = 36 days. So the correct answer is 36 days, which corresponds to option D. The initial correction was wrong; the original correct_answer D is correct.

The total work can be calculated as 12 men × 8 hours/day × 10 days = 960 man-hours. To complete the same work in 5 days working 12 hours a day, the number of men required is 960 ÷ (12 hours/day × 5 days) = 16 men.

P's work rate is 1/16 per day, Q's is 1/12 per day. Together with R, they complete the job in 4 days, so combined rate is 1/4 per day. R's rate = (1/4) - (1/16 + 1/12) = 1/4 - (3/48 + 4/48) = 1/4 - 7/48 = 12/48 - 7/48 = 5/48. Therefore, R alone takes 48/5 = 9.6 days, which is 9(3/5) days.

The total work done by 6 men in 2 days is 6 × 2 = 12 man-days, which produces 10 sofas. Therefore, the man-days required to make one sofa is 12 ÷ 10 = 1.2 man-days. For 8 sofas, the total man-days required is 8 × 1.2 = 9.6 man-days. With 8 men working, the number of days required is 9.6 ÷ 8 = 1.2 days. Hence, the correct answer is 1.2 days, which corresponds to option C.

Let the work done by P, Q, and R per day be p, q, and r respectively. From the given: p + q = 1/30, q + r = 1/24, r + p = 1/20. Adding all three: 2(p + q + r) = 1/30 + 1/24 + 1/20 = (4 + 5 + 6)/120 = 15/120 = 1/8, so p + q + r = 1/16. After 10 days working together, work done = 10 × 1/16 = 10/16 = 5/8. Remaining work = 3/8. Since Q and R left, only P works now at rate p = (p + q + r) - (q + r) = 1/16 - 1/24 = (3 - 2)/48 = 1/48 per day. Time for P to finish remaining work = (3/8) ÷ (1/48) = 18 days. However, the calculation shows 18 days, but the options have 8 as B and 18 as C. Rechecking: p = (p + q + r) - (q + r) = 1/16 - 1/24 = (3/48 - 2/48) = 1/48. Remaining work = 3/8. Time = (3/8) / (1/48) = (3/8) × 48 = 18 days. So correct answer is C (18). The original answer was correct. The explanation was missing and difficulty was not set; difficulty is medium. Tags added for clarity.

Given: 10 men can complete the work in 7 days, so the work done by 10 men in 1 day is 1/7. Therefore, work done by 1 man in 1 day is (1/7)/10 = 1/70. Similarly, 10 women can complete the work in 14 days, so work done by 10 women in 1 day is 1/14. Therefore, work done by 1 woman in 1 day is (1/14)/10 = 1/140. Now, work done by 5 men in 1 day = 5 × (1/70) = 1/14. Work done by 10 women in 1 day = 10 × (1/140) = 1/14. Total work done by 5 men and 10 women in 1 day = 1/14 + 1/14 = 1/7. Hence, the total number of days required to complete the work = 1 / (1/7) = 7 days. Therefore, the correct answer is 7 days, which corresponds to option A.