25 men and 45 women can complete a piece of work in 15 days, while 15 men and 50 women can complete it in 20 days. In how many days can 69 men and 67 women complete the work ?

6

25M + 45W = 15D     

375M + 675W = 01D          ..(1)       (Multiplied by 15 to get it done in 1 day)

15M + 50W = 20D

300M + 1000W = 01D        ..(2)        (Multiplied by 20 to get it done in 1 day)

Now, (1) - (2), we get

⇒ 75M = 325W

⇒ M : W = 325 : 75 = 13 : 3 (Efficiencies)

Putting efficiency in equation (2), and we get the total work 

⇒ [300 (13) + 1000(3)]

⇒ 6900

Now, total efficiency of 69M+67W = 69 (13) + 67 (3) = 897 + 201 = 1098

Required time = \(\frac{Total work}{efficiency}\) = \(\frac{6900}{1098}\) = 6.28 days ~ 6days