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?
Answer & explanation
Correct answer: option 2
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 %