Time and Work

Makarand takes 27 days, so his rate is 1/27. Samarjit is twice as fast, so his rate is 2/27. Together, their rate is 1/27 + 2/27 = 3/27 = 1/9. They will finish the job in 9 days.

Total work = 40 * 18 = 720 man-days. Work done in 8 days = 40 * 8 = 320. Remaining work = 720 - 320 = 400. New number of men = 40 + 10 = 50. Days for remaining work = 400 / 50 = 8.

A does 1/9 per day, B does 1/15. In 2 days, they do 1/9 + 1/15 = 8/45. In 10 days (5 cycles), they do 40/45. On the 11th day, A does 1/9 = 5/45. Total = 45/45. Work finished in 11 days.

Rambo finishes 3/5 of the work in 9 days, so he does 1/15 of the work per day. In the next 4 days, Rambo and Shaun finish the remaining 2/5 of the work. Thus, (Rambo + Shaun) rate = (2/5) / 4 = 1/10 per day. Shaun's rate = 1/10 - 1/15 = 3/30 - 2/30 = 1/30. Shaun takes 30 days to finish the work alone.

Chainu rate = 1/30. Pinky rate = 1/40 (half in 20 days). Work done: Chainu (10/30) + Pinky (8/40) = 1/3 + 1/5 = 8/15. Remaining work = 7/15. Disha does 7/15 in 21 days, so Disha rate = (7/15) / 21 = 1/45. Disha takes 45 days.

A's rate = 1/24, B's rate = 1/16. (A+B+C)'s rate = 1/8. C's rate = 1/8 - (1/24 + 1/16) = 1/8 - (2/48 + 3/48) = 6/48 - 5/48 = 1/48. C takes 48 days.

A's rate = 1/36, B's rate = 1/48. Together = 1/36 + 1/48 = 7/144. In 8 days, they do 8 * 7/144 = 56/144 = 7/18. Remaining = 11/18. A takes (11/18) / (1/36) = 11 * 2 = 22 days.

Work = 50 * 28 = 1400 units. Days 1-10: 50 * 10 = 500. Days 11-20: 40 * 10 = 400. Days 21-30: 30 * 10 = 300. Days 31-40: 20 * 10 = 200. Total = 500+400+300+200 = 1400. Completed in 40 days.

Let N take x days. M takes 1.6x days. Their rates are 1/x and 1/(1.6x). Together: 1/x + 1/(1.6x) = 1/24. (1.6 + 1) / 1.6x = 1/24. 2.6 / 1.6x = 1/24. 2.6 * 24 / 1.6 = x. x = 39.

A's rate = 1/10, B's rate = 1/20. Together A+B+C = 1/5. C = 1/5 - (1/10 + 1/20) = 1/5 - 3/20 = 4/20 - 3/20 = 1/20. C takes 20 days.

8M = 17W, so 1M = 17/8 W. 12M + 24W = 12*(17/8)W + 24W = 25.5W + 24W = 49.5W. 17 women take 33 days for 1 house, so 1 woman takes 17*33 days for 1 house. 49.5 women take (17*33)/49.5 days for 1 house = 11.33 days. For 3 houses, time = 11.33 * 3 = 34 days.

Sagar completes the job in 18 days (rate = 1/18). Madhur is 2 times faster (rate = 2/18 = 1/9). Together, their rate is 1/18 + 1/9 = 3/18 = 1/6. They finish in 6 days.

P's rate = 1/50, Q's rate = 1/20. Combined rate = 1/50 + 1/20 = 7/100. Time to complete 70% of the task = (0.7) / (7/100) = 0.7 * 100 / 7 = 10 days.

If Akash is 3 times as fast as Baldev, the ratio of time taken is 1:3. Let Baldev take 3x and Akash take x. 3x - x = 40, so x = 20. Akash takes 20 days, Baldev takes 60. Together, they take (20*60)/(20+60) = 1200/80 = 15 days.

Let Badal take x days, then Amar takes x/2 days. x - x/2 = 15, so x/2 = 15, x = 30. Amar takes 15 days, Badal takes 30 days. Together: 1/15 + 1/30 = 3/30 = 1/10. They take 10 days.