# Aptitude - Time and Work - Discussion

### Discussion :: Time and Work - General Questions (Q.No.15)

15.

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

 [A]. 3 [B]. 5 [C]. 7 [D]. Cannot be determined [E]. None of these

Explanation:

 1 woman's 1 day's work = 1 70

 1 child's 1 day's work = 1 140

 (5 women + 10 children)'s day's work = 5 + 10 = 1 + 1 = 1 70 140 14 14 7 5 women and 10 children will complete the work in 7 days.

 Deepti said: (Aug 25, 2010) How can we write 5 women's and 10 children's 1 day work is 5/70 and 10/140?

 Kamlesh Jaiswal said: (Sep 2, 2010) 10 women's one day work =1/7 So 1 women's one day work =1/70 So 5 women's one day work =5*1/70 Similarly, 1 child's one day work = 1/140 and 10 child's one day work = 10/140

 Mahesh said: (Sep 9, 2010) 10 women's one day work =1/7 So 5 women's one day work=1/14 and 10 child's one day work =1/14 So 5 women's and 10 childrens one day work is = 1/14 + 1/14 = 2/14 = 1/7 Ans: 7 days.

 Swamy said: (Nov 1, 2010) 1 women= 2 childrens so 5 women+ 10 children=10 women = 7days

 Kannips said: (Dec 12, 2010) Mahesh realy super.

 Santh said: (Dec 27, 2010) Swamy. Good.

 Jyothi said: (Jan 25, 2011) hi swamy super ur brilliant

 Manikandasenthil said: (Apr 11, 2011) Can any one explain this... 10 women can do the work in 7 days why can't 5 women can do the work in 7/2 days I solved it this way and it is not working... what goes wrong in the middle?? 5 women one days' work = 1/(7/2) = 2/7 10 children one days' work = 1/14 2/7 + 1/14 = 98/35??

 Pranathi said: (May 31, 2011) @Manikandasenthil; when u do 7/2 u r not decreasing the no of women working , but u r decreasing the work they do. just use a simple logic........... when u reduce the no of people wrking the time taken to complete it will increase.......... in that case when u do 7/2 it either appears that the wrk done is reduced to half or, that u hav doubled the no of women wrking.......

 Pranil said: (Jun 2, 2011) Yes this is a good ans.

 Ali Umar said: (Aug 3, 2011) Thanks. Samy super mind.

 Asha said: (Sep 16, 2011) Well 10 women can complete a work in 7 days and 10 children can do it in 14 days, that means one woman is 2 times efficient than a child therefore 1woman=2 children, therefore 10 children+10 children(or 5 women) can do a work in 14/2 i.e. 7 days.

 Karthik Kovai said: (Feb 2, 2012) Let simply x be the woman's 1 day work. y be the children's 1 day work. so, 10x= 1/7 ; 10y= 1/14 x= 1/70 ; y= 1/140 then 5*1/70 = 1/14 ; 10*1/140 =1/14 1/4 + 1/4 =1/7 So they will take 7 days to complete.

 Sam said: (Feb 26, 2012) If ratio is 1:2 then (women * women working days/children) i.e 10*7/10=7

 Jyoti said: (Mar 22, 2012) Short and fast 70w=140c 1w=2c m1d1=m2d2 10X14=20Xd2 d2=7days ans.

 Jitendra Gupta said: (Mar 28, 2012) Here what we can simply do as follows! Convert the work into Woman Days (WD) and Children Days (CD) WD - 7*10 = 70 CD - 14*10 = 140 It means 1 woman is equal to 2 Children. so now convert woman into children. Means 5 Woman equal to 10 Children + No. of Children Children Days/No. of Children 140/20 = 7 Days

 Kulbhushan Chaskar said: (May 28, 2012) 10 W =7 .. 5 W =14 10 C =7 .. 10C =14 1 day work of 5W+10C=1/14+1/14 1/14+1/14=1/7 Hence 7 days.

 Ravi said: (Jun 8, 2012) 10 women in 7 days.then v can alsov say 5 women in 14 days. also 10 children in 14 days. therfore 1women=2 children. Now 5 women and 10 children are 20 children(as 1women =2 children). As 10children in 10days therefore 20 children in 7 days.

 Disha said: (Aug 20, 2012) Love your way to solve the problem. Swamy. Superb brain.

 Medha Bhatnagar said: (Feb 1, 2013) One more way to do this prob. 5* (1/70) +10* (1/140) =2/14=1/7=7 days.

 Rox said: (Sep 26, 2013) 10 women in 7 days. 5 women(A) in 14 days. A = (1/14). 10 child(B) in 14 days(given). B = (1/14). A+B = (1/14+1/14) = 2/14 = 1/7. That is 7 days.

 Deepak Patgar said: (Aug 23, 2014) 10 women need 7 days, so 5 women need 14 days. 10 children need 14 days. So if 5 women and 10 children work together for 14 days they will complete the work twice. To complete it once they will need 14/2 = 7 days.

 Ranjan said: (Nov 14, 2014) 10 WOMEN CAN DO THE WORK IN 7 DAYS. THEN 5 WOMEN CAN DO THE WORK IN 14 DAYS. AND 10 CHILDREN CAN DO THE WORK IN 14 DAYS. SO 5 WOMEN+10 CHILDREN CAN DO THE WORK IN 14*14/14+14 = 7 DAYS.

 Shiva said: (Nov 30, 2014) 10 children 14 days. 20 children 7 days. => 1w = 2c. => 10c = 5w. => 5w+10c = 5w+5w = 10W. So 10w complete in 7 days given in question.

 Sai Krupa said: (Mar 28, 2015) Its always better to take LCM for the total times which gives the total amount of work. So then solve the sum its so simple.

 Priya said: (May 18, 2015) How to use LCM method for this problem please explain?

 R_Pandya said: (Sep 4, 2015) Take one women's one day's work = x; One child's one day's work = y; 10 women can complete the work in 7 days. So 10x = 1/7. Similarly 10y = 1/14. Now take this value in the equation for 5 women and 10 children's work. 5x+10y = 5(1/70)+1/14 = 1/7. So the total work done in 7 days.

 Sekhar said: (Dec 13, 2015) 10 women 1 day work = 1/7. 1 women 1 day = 1/70. Like wise 1 child 1 day work = 1/ 140. 5 women + 10 children can do work in? = 1/70*5+1/140*10 = 1/14+1/14 = 7 days.

 Ajit Kumar said: (Mar 14, 2016) Dear ManikandSenthil, If we reduce the number of people, then it will take more time 2 do the same work. Like for ex: In above question it is given that 10 women can do 1 work in 7 days, then if we reduce its number, more day it requires 2 do the same work. It is indirectly proportional 2 each other.

 Ashish said: (Apr 17, 2016) Lets 1-day work for women be x, and 1-day work for children be y. Now, 10 women and 10 children 1 day work will be 10x =1/7 --> equation 1. 10y =1/14 --> equation 2. Now, 5 women and 10 children 5x +10y = ? --> equation 3. Take equation 1 (divide by 2) and equation 2 and put it in equation 3. 1/14 + 1/14 = 1/7. So, it will take 7 days.

 Thenmozhi said: (Apr 18, 2016) Thanks for explaining the answer in different ways. Thank you all.

 Surya Prakash said: (Jun 15, 2016) 10 women do in 7 days. 10 children can do in 14 days. So 1 women = 2 children. => 10 children = 5 women. So total we have 10 women (5 women and 10 children). Given 10 women can do it in 7 days. So, it will take 7 days.

 Math said: (Jul 18, 2016) Explanation. 1st Point : 05 women work. 10 woman 01 day work 1/7part. 01 woman 01 day work 1/7x10 = 1/70part. 05 woman 01 day work 1x5/70 = 5/70 = 1/14part. -> 05 woman work 1/14. 2nd Point: 10 Children Work. 10 children 01 day work = 1/14part. ->10 Children work = 1/14. 3rd Point : How many days will 5 women and 10 children take to complete the work? 05 Women work means = 1/14 (1st Point answer). 10 children work means = 1/14 (2nd Point answer). -> 05 Women + 10 children = 1/14 + 1/14 = 2/14 = 1/7. -> 05 Women + 10 children 1/7 part work done 1days. -> 05 Women + 10 children 1 part work done 7 days. Answer : 7 days.

 Suraj Dev said: (Sep 20, 2016) It has simple formula. a = 10, x = 7, b = 10, y = 14, c = 5, d = 10. No of days = 1/((c/ax) + (d/by)). Ans = 7 days.

 Sandeep said: (Jan 5, 2017) 10 women work = 1/7 = 5womens can doing(1/3.5). 10 boys work = 1/14. So we want 5womens + 10 boys work = 5 * (1/3.5) + 10(1/14). Solving we can get answer approximately 7.

 Vivek said: (Aug 2, 2017) Can some one do it in LCM method?

 Ritzie said: (Sep 30, 2017) It can be done by L.C.M method, but it will be a long method for this particular ques. L.C.M (7,14)days= 14 units of work, for women, in 7 days, 10 women=14 units of work =>1 women work=14/10 units of work ( in 7 days) therefore, 1-day work of 1 woman =14/(10*7) = 1/5 units of work for children, in 14 days, 10 children=14 units of work =>1 child work=14/10 units of work ( in 14 days) therefore, 1-day work of 1 child =14/(10*14) = 1/10 units of work 1 day work of (5 woman+ 10 children) = (1/5)*5 + (1/10)*10 = 2 units of work But the work to be done is 14 units thus this work can be done in => 14/2 = 7 days.

 Gouri said: (Nov 21, 2018) 10W =>7 days. 10C =>14 days. 5W+10C = ?. LCM of 7&14 is 14. The efficiency of 10W is 2 and the efficiency of 10C is 1. So, for 5W efficiency required is only 1 & for 10C efficiency is 1. ie; 1 + 1 = 2. 14/2 = 7days (here 14 is LCM).

 Navi said: (Jan 9, 2019) 10 women= 1/7 th work per day. Then; 1 women= 1/70th work per day. -------> (1) in the same way 1 child = 1/140th work per day -----------> (2) So 5(w) + 10(c) = 5(1/70) + 10(1/140) ;from (1) and (2) 1/14+1/14 = 2/14 = 1/7. So 1/7th work is done per day by 5 women and 10 children. Hence they will take 7 days to complete whole work.

 Sujesh K said: (Jul 22, 2019) This can be done by equating the given datas, Let's assume x be women and y be children, From the question, 10x = 1/7(1-day work)---> (1) 10y = 1/14(1-day work)---> 2) 5x+10y=?---> (3) From (1), 2(5x)=1/7 5x=1/14 ---> (4). Therefore, substitute (2) and (4) in (3). We get 5x+10y=1/14 + 1/14. = 2/14 = 1/7. So it takes 7 days to complete.

 Nouf said: (Aug 28, 2019) 10 W = 70 W. 10 Child 140 W. 1W =2 Child. => 5W+10 C= 5+5 Women = 7 days.