Time and Work

Boy's rate = 1/(20*25) = 1/500 work/day. Girl's rate = 1/(25*22) = 1/550 work/day. Combined rate = 20*(1/500) + 25*(1/550) = 20/500 + 25/550 = 1/25 + 1/22 = (22+25)/550 = 47/550. Time = 550/47 = 11.7 days, which is approximately 12 days.

1 girl takes 100 days, so 1 girl's work rate is 1/100 per day. 10 boys + 15 girls take 6 days, so their combined rate is 1/6 per day. 15 girls' rate is 15/100 = 3/20. 10 boys' rate = 1/6 - 3/20 = 10/60 - 9/60 = 1/60. Thus, 1 boy's rate = 1/600, meaning 1 boy takes 600 days.

1 man's work per day = 1/70. 1 girl's work per day = 1/140. 8 men + 10 girls = 8/70 + 10/140 = 16/140 + 10/140 = 26/140 = 13/70. Time = 70/13 = 5.38 days, which is approximately 5.40.

Work rates: Boy=1/30, Girl=1/60, Woman=1/80. Total work needed in 3 days = 1. Work done by 4 boys and 6 girls in 3 days = 3 * (4/30 + 6/60) = 3 * (2/15 + 1/10) = 3 * (4/30 + 3/30) = 3 * (7/30) = 21/30 = 7/10. Remaining work = 3/10. Let w be number of women: w * (1/80) * 3 = 3/10. w/80 = 1/10, w = 8.

Let B and G be daily wages. 16(4B + 2G) = 10(4B + 5G). 64B + 32G = 40B + 50G. 24B = 18G. G = (24/18)B = (4/3)B. If B = 800, G = (4/3) * 800 = 1066.66.

Let x be the number of women. Work = x * 50. If there are x+10 women, work = (x+10) * 46. So 50x = 46x + 460. 4x = 460, x = 115.

Let Q's time be t. P's time is t/3. t - t/3 = 40, so 2t/3 = 40, t = 60. P takes 20 days, Q takes 60 days. Together: 1/20 + 1/60 = 4/60 = 1/15. They take 15 days.

Let R, S, J be work rates. R = S + J. Given R + S = 1/10 and J = 1/50. Substituting R: (S + J) + S = 1/10 => 2S + 1/50 = 5/50 => 2S = 4/50 => S = 1/25. Shyam takes 25 days.

Let P, S, V be the work rates. P+S=1/24, S+V=1/30, V+P=1/40. Summing these gives 2(P+S+V) = 1/24 + 1/30 + 1/40 = (5+4+3)/120 = 12/120 = 1/10. Thus P+S+V = 1/20. P = (P+S+V) - (S+V) = 1/20 - 1/30 = 1/60. Prem takes 60 days.

Using the work-worker formula, 36 * 14 = X * 8. Solving for X gives X = (36 * 14) / 8 = 63 total workers. The additional workers required are 63 - 36 = 27.

Kashish takes 32 days. Vibhu is 60% more efficient, meaning Vibhu's efficiency is 1.6 times Kashish's. Days taken by Vibhu = 32 / 1.6 = 20 days.

A finishes 1/3 in 5 days, so A's rate is 1/15. G finishes 2/5 in 10 days, so G's rate is 2/50 = 1/25. Combined rate = 1/15 + 1/25 = 5/75 + 3/75 = 8/75. Time = 75/8 = 9.375 days, which is 9 and 3/8 days.

6 men = 4 days, so 1 man = 24 days. 8 women = 4 days, so 1 woman = 32 days. 3 men work for 2 days = 3 * 2 / 24 = 6/24 = 1/4 of work. Remaining work = 3/4. 3/4 work in 3 days = 1/4 work per day. 1 woman does 1/32 work per day. Number of women = (1/4) / (1/32) = 8 women.

Mahesh is 1/5 more efficient than Ramesh, meaning Mahesh's efficiency = 1 + 1/5 = 6/5 of Ramesh's. If Ramesh takes 42 days, Mahesh takes 42 / (6/5) = 42 * 5 / 6 = 35 days.

P: 1/4 work in 10 days -> 1 work in 40 days. Q: 0.4 work in 40 days -> 1 work in 100 days. R: 1/3 work in 13 days -> 1 work in 39 days. R takes the least time.