It takes 10 men and 6 women to finish a work in 4 days , while it takes 5 men and 7 women to finish the same job in 6 days .what will be the time taken by 1 man and 1 women?
Answers
Step-by-step explanation:
Given:
It takes 10 men and 6 women to finish a work in 4 days , while it takes 5 men and 7 women to finish the same job in 6 days
To Find:
What will be the time taken by 1 man and 1 women
Solution:
10 men and 6 women can do the work in = 4 days
(10×4) men and (6×4) women can do the work in = 1 day
40 men and 24 women can do the work in = 1 day
5 men and 7 women can do the work in = 6 days
(5×6) men and (7×6) women can do the work in = 1 day
30 men and 42 women can do the work in =1 day
So,. both are equal
40 men + 24 women=30 men+42 women
40 men - 30 men= 42 women - 24 women
10 men=18 women
1 man=18/10=9/5 women
We can put it in any.
If 1 men =9/5 women
So, 10 men=9/5×10=18 women
10 men and 6 women=18+6=24 women
If 1 man=9/5 women
1 man and 1 woman=9/5+1=9+5/5=14/5 women
24 women can do the work in = 4 days
1 woman and do the work in = (4×24) days
14/5 women can do the work in =4×24×5/14
→240/7 days.
So 1 man and 1 woman can do the work in 240/7 days
Solution :
• It takes 10 men and 6 women to finish a work in 4 days
• It takes 5 men and 7 women to finish the same in 6 days.
We have to find the time taken to complete the job by 1 man and 1 women to complete that Job .
10 men and 6 women take 4 days to finish it.
> 10 men and 6 women can do ¼th of the work in 1 day
> 5 men and 7 women can do ⅙th of the work in 1 day .
Let us assume men as a and women as b
> 10a + 6b = ¼ and 5a + 7b = ⅙th
Multiplying the second equation by 2
> 10a + 14b = ⅓.
Subtracting the first eqn from this one
> 8b = ⅓ - ¼ = ¹/12
> b = 1/96
> 1 women takes 96 days to complete the work.
{ Hence 6 women take 1/16 days }
> 10a + 1/16 = 1/4
> 10a = 3/16
A man takes 160/3 days
work done by 1 man and 1 women in a day
> 1/96 + 3/160
> 1/32( 1/3 + 3/5)
> 1/32( 14/15)
Time taken by 1 man and 1 women to complete the work -
> ≈ 34 days
The time taken by 1 man and 1 women to complete the work is 34 days .
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