Question

8 women and 12 men can together finish a work in 10 days while woman in 8 minutes can finish at 14 days find the time taken by one woman alone to finish the work that also what taken by one man alone ?​

Answer 1

Step-by-step explanation:

Given that: 8 women and 12 men can together finish a work in 10 days while 8 woman can finish in 14 days. find the time taken by one woman alone to finish the work that also what taken by one man alone ?

To find: the time taken by one woman alone to finish the work that also what taken by one man alone ?

Solution: Let the time taken by 1 woman is x days

and time taken by 1 man is y days.

So, one day work of one woman is (1/x)th part of the work.

one day work of 8 women is (8/x)th part of the work.

one day work of a man is (1/y)th part of the work.

one day work of 12 men is (12/y)th part of the work.

So, we can write

$\frac{8}{x} + \frac{12}{y} = \frac{1}{10} \: \: \: \: ...eq1$

because 8 women finish the work in 14 days,so one day work of 8 women

$\frac{8}{x} = \frac{1}{14} \: \: \: ...eq2$

Put value of eq2 in eq1

$\frac{1}{14} + \frac{12}{y} = \frac{1}{10} \\ \\ \frac{12}{y} = \frac{1}{10} - \frac{1}{14} \\ \\ \frac{12}{y} = \frac{14 - 10}{140 } \\ \\ \frac{12}{y} = \frac{4}{140} \\ \\ \frac{12}{y} = \frac{1}{35} \\ \\ y = 12 \times 35 \\ \\ y = 420$

From eq2, by cross multiplication

One woman alone can finish the work in 8×14 i.e. 112 days.

One man alone finish the work in 420 days.

Hope it helps you.

Answer 2

Given :  8 women and 12 men can together  finish a work in 10 days, while 6  women and 8 men can finish it in 14  days.

To  Find : the time taken by 1  woman alone to finish the work, and

also that taken by 1 man alone.​

Solution :

Let say Man 1 day work = M

& woman 1 day work  = W

Total Work 8 women and 12 men can together finish a work in 10 days

=> 8W  * 10 + 12M * 10    = 80W + 120M     Eq1

Total Work 6 woman and 8 man can together finish a work in 14 days

=> 6W * 14  + 8M * 14 =  84W  +  112M       Eq2

Equating total work  Eq 1 = Eq2

80 W + 120M = 84W + 112M

=> 8M = 4W

=> 2M = 1W

Substitute in Total work Eq 1

Total work =  80(2M) + 120M  = 280 M  

Hence one man can finish work alone in 280 days

280 M = 140 * 2M = 140W

Hence  woman alone can finish in 140 days

Learn More:

3 men and 4 women can complete a work in 16days while 4 men ...

https://brainly.in/question/11701323

An amount of ₹ 121.55 is to be distributed as wages amongst a man ...

https://brainly.in/question/8796897