Two men and 10 women working together can do a job in 15 days. The same job is done by 6 men in 'X' days and 20 women in 'X+5' days. Find efficiency of women is how much % of a man?

20%

Total work = Efficiency × Number of days

(2M + 10W) × 15 = Total work

           total work   = 30M + 150W

According to question ,

         6M X = 20 W (X+5)

  ⇒     6M  = \(\frac{20W}{X}\) (X + 5) ------ (i)

        30 M + 150 W = 6 MX  (Total work is same)

     150 W =  6M X - 30 M

     150 W = 6M [X-5]   ------ (ii)

    Put the value of 6M from eqn (i) in eqn (ii)

      150 W = \(\frac{20W}{X}\) (x+5) (X-5)

       15W X = 2W (X+5) (X-5)

       15 X = 2 (X² - 25)

        2X² - 15X - 50 = 0

     After solving X = 10

from eqn (i)  6M = \(\frac{20 W}{10}\) (10+5)

          6M = 2W × 15

  ⇒     \(\frac{M}{W}\) = \(\frac{5}{1}\)

 Required % = \(\frac{1}{5}\) × 100 = 20 %