b)5 men can do equal amount of work as 8 women. If 3 men and 5 women

combinely do job in 10 days, then how many woman required to finish it in
14 days?

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5 men = 8 women(in terms of working capability)------[1]

now,3men + 5 women = 10.
their 1 day's work is:
3 men + 5 women = 1/10
=>30 men + 50 women = 1--------[2]
from [1],1 men = 8/5 women----[3]
[3] in [2],
30*8/5 women + 50 women = 1.
=>(48+50) women = 1.
=>98 women = 1.
that means, 98 women can do the work in 1 day.
therefore, in 14 days = 98/14 women can do it.
= 7 women.

To solve this problem, we need to first determine the rate at which one man and one woman can complete the job. Let's assume that one man can complete the job in "M" days, and one woman can complete the job in "W" days.

Given that 5 men can do the same amount of work as 8 women, we can set up a ratio:

5M = 8W

Next, we are told that 3 men and 5 women together complete the job in 10 days. We can set up another ratio:

(3M + 5W) * 10 = 1

To solve for "M" and "W", we can substitute the ratio from the first statement into the second equation:

(3(8W/5) + 5W) * 10 = 1

Simplifying this equation will give us the value of "W." Let's solve it step by step:

First, distribute the 3 to the terms inside the parentheses:
(24W/5 + 5W) * 10 = 1

Next, combine like terms:
(24W + 25W) * 10 = 1

Further simplification:
49W * 10 = 1

Multiply both sides by 10 to isolate W:
490W = 1

Divide both sides by 490:
W = 1/490

Now we know that one woman can complete 1/490th of the job in a day.

To determine how many women are required to complete the job in 14 days, we need to calculate the fraction of the job that can be completed in one day by one woman.

Since we know one woman can complete 1/490th of the job in a day, we can calculate the fraction of the job that can be completed in 14 days:

(1/490) * 14 = 14/490 = 1/35

Therefore, in order to finish the job in 14 days, we would need 1 woman.