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 women are there in the family
Choose the correct answer: A) 1 B) 2 C) 3 women D) 4 E) 5
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= 
<gadget id="calculator"> 360/120</gadget>
<output>3</output>
3 units per day   1 woman does 360/180= 
<gadget id="calculator">360/180</gadget>
<output>2</output>
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= 
<gadget id="calculator">15-12</gadget>
<output>3</output>
3   ANSWER:3 women
<result>C</result>
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 women are there in the family