Math, asked by gurunathbidave, 7 hours ago

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

Answered by Anonymous
4

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

Answered by Saby123
7

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 .

________________________________________

Similar questions