Aptitude - Time and Work - Discussion

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 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.

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.

@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.......

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.

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.

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

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.

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.

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??