Aptitude - Time and Work - Discussion

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

Answer: Option C

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.

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