Aptitude - Time and Work - Discussion

Thanks for explaining the answer in different ways. Thank you all.

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.

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.

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.

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.

Can some one do it in LCM method?

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.

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).

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.

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.