4 men and 10 women were put on a work. They completed 1/3 of the work in 4 days. After this 2 men and 2 women were increased. They completed 2/9 of the work in 2 days. If the remaining work needs to be completed in 3 days, how many more women need to be increased?

Let one man's work per day be 'm' and one woman's work per day be 'w'. Total work = T. First phase: 4(4m + 10w) = T/3, so 4m + 10w = T/12. Second phase: 2(6m + 12w) = 2T/9, so 6m + 12w = T/9. Solving: From first eq, 12m + 30w = T/3. From second eq, 18m + 36w = T/3. Equating: 12m + 30w = 18m + 36w, so -6m = 6w, or m = -w. This seems wrong. Let me recalculate. Actually: 4 days of (4m+10w) = T/3, so (4m+10w) = T/12. And 2 days of (6m+12w) = 2T/9, so (6m+12w) = T/9. From first: 12m + 30w = T/3. From second: 18m + 36w = T/3. Subtracting: 6m - 6w = 0, so m = w. Then T = 12(4m + 10m) = 12(14m) = 168m, or T = 9(6m + 12m) = 9(18m) = 162m. Hmm, inconsistency. Let me use the second eq: T = 9(6m + 12w) = 54m + 108w. From first eq: 4m + 10w = T/12 = (54m + 108w)/12 = 4.5m + 9w. So 4m + 10w = 4.5m + 9w, giving w = 0.5m. Then T = 54m + 108(0.5m) = 54m + 54m = 108m. Work done so far = T/3 + 2T/9 = 3T/9 + 2T/9 = 5T/9. Remaining = 4T/9 = 4(108m)/9 = 48m. Current team: 6m + 12w = 6m + 12(0.5m) = 6m + 6m = 12m per day. In 3 days: 3 × 12m = 36m. Need 48m - 36m = 12m more. Adding x women: new rate = 12m + xw = 12m + 0.5xm. In 3 days: 3(12m + 0.5xm) = 36m + 1.5xm = 48m. So 1.5xm = 12m, x = 8. Option D is correct.