There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many men and women are there in the family

• Let the number of men be m and so the number of women = 15-m
  Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start.
  Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days).
  
  Let the total work be 360 units (LCM of 180 and 120).
  1 man does 360/120 = 3 units per day
  1 woman does 360/180 = 2 units per day
  
  Based on above facts,
  Total work by men + women in these 17 days = 360 units
  m*9*3 + (15-m)*6*2 = 360,
  27m + 180 -12m = 360, Solving m=12.
  Num of men = 12 and number of women = 15-12 = 3
• 10 years agoHelpfull: Yes(37) No(2)
• i think 10 mens and 5 womens are in the family.
  
• 11 years agoHelpfull: Yes(4) No(2)
• laura mera
  
• 9 years agoHelpfull: Yes(3) No(3)
• I think 6 women and 9 men.
  let number of women=w and number of men= m.
  w--->180 days
  m--->120 days
  then both can do means w+m=15 given can do work in 72 days.
  ==> 15--->72 days
  w--->180 days
  ==> w= 15*(72/180)=72/12=6
  w+m=15,6+m=15,m=9
• 11 years agoHelpfull: Yes(1) No(6)
• let there are x men. that implies women are (15-x)
  let no . of days they work together is d.
  x*d=120
  (15-x)d=180
  on solving, d=20 days,
  =>x=6=no. of men
  w=(15-6)=9 women.
• 10 years agoHelpfull: Yes(1) No(0)