4 men and 7 women can complete a work in 9 days while working together, whereas 6 men and 5 women can complete this work in 6 days , find in how many days work will be finished by 5 men and 6 women ?

Let m = one man's daily work, w = one woman's daily work. 4m + 7w = 1/9 and 6m + 5w = 1/6. Solving: multiply first by 3: 12m + 21w = 1/3. Multiply second by 2: 12m + 10w = 1/3. Subtracting gives 11w = 0, so w = 1/110, m = 1/10. For 5m + 6w: 5(1/10) + 6(1/110) = 1/2 + 6/110 = 61/110 per day. Days = 110/61 ≈ 7.2 days. Option D is incorrect - the system is solvable.