Question

3 men & 7 women can complete a work in 10 days, while 4 men and 6 women can complete it in 8 days. In how many days will 10 women complete it?

Answer 1

If a man can do it in m days, and

a woman can do it in w days, then
3/m + 7/w = 1/10
4/m + 6/w = 1/8
Solve for w and then you want w/10

Answer 2

sir,

l got on solving 6w = 1/40
1w = 1/240
so 10w = 1/240 x 10 =1/24
= 24 days .
ls it correct sir.

Answer 3

I think w=400

3/m + 7/w = 1/10
4/m + 6/w = 1/8
now use elimination.
12/m + 28/w = 2/5
12/m + 18/w = 3/8
-------------------------
10/w = 1/40
w = 400
So it will take 10 women 40 days.

Answer 4

Hmmm. That doesn't make sense. You may be right after all. I'll have to double-check.

Answer 5

Nope. w=400 days is right. That means that the women basically do nothing, which agrees roughly with the data. If the women really do nothing, then

If 3 men can do it in 10 days, then 4 men can do it in 7.5 days, which is just about what they have said.

Answer 6

[AI-generated answer — Explain Bot]

To solve this problem, we can use the concept of "man-days" and "woman-days." Let's start by assigning variables to represent the amount of work done by each man and each woman in one day.

Let's assume that a man can complete 1 unit of work in one day (1 man-day), and a woman can complete 1 unit of work in one day (1 woman-day).

From the given information, we can create two equations:

Equation 1:
"3 men and 7 women can complete the work in 10 days"

3(man-days) + 7(woman-days) = 10 days

Equation 2:
"4 men and 6 women can complete the work in 8 days"

4(man-days) + 6(woman-days) = 8 days

Now, let's solve these equations simultaneously to find the values of man-days and woman-days.

Equation 1:
3(man-days) + 7(woman-days) = 10
=> 3(man-days) = 10 - 7(woman-days)
=> 3(man-days) = 10 - 7(woman-days)
=> man-days = (10 - 7(woman-days))/3

Equation 2:
4(man-days) + 6(woman-days) = 8
=> 4(man-days) = 8 - 6(woman-days)
=> man-days = (8 - 6(woman-days))/4

Now, we can equate the two expressions for man-days and solve for woman-days:

(10 - 7(woman-days))/3 = (8 - 6(woman-days))/4

Cross-multiplying:

4(10 - 7(woman-days)) = 3(8 - 6(woman-days))

Simplifying:

40 - 28(woman-days) = 24 - 18(woman-days)

Moving terms with woman-days to one side:

40 - 24 = 28(woman-days) - 18(woman-days)

16 = 10(woman-days)

Dividing both sides by 10:

woman-days = 16/10 = 1.6 woman-days

Since we cannot have a fraction of a day, we can consider that one woman takes 2 days to complete the work.

Now, to find how many days will 10 women complete the work, we can divide the total work by the number of women:

10 women * 2 days/woman = 20 days

Therefore, 10 women will take 20 days to complete the work.