5 men and 8 women can complete a task in 34 days, whereas 4 men and 18 women can complete the same task in 28 days. In how many days can the same task be completed by 3 men and 5 women?

Answer: Option C

(5M + 8W) × 34 = (4M + 18W) × 28
85M + 136W = 56M + 252W
29M = 116W
$$\frac{\text{M}}{\text{W}}=\frac{4}{1}$$
(5M + 8W) × 34 = (3M + 5W) × x
(5 × 4 + 8 × 1) × 34 = (3 × 4 + 5 × 1) × x
28 × 34 = 17 × x
x = 56 days