Aptitude - Time and Work - Discussion

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.

Can some one do it in LCM method?

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.

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.

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.

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.

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

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.

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.

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.