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20 men can complete a work in 14 days and 20 women can complete the same work in 18 days. 8 men start the work and after working for 21 days, they are replaced by x women. If the remaining work is to be completed by x women in 9 days, then how many women should be employed?
- a)18
- b)24
- c)20
- d)16
- e)15
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
20 men can complete a work in 14 days and 20 women can complete the sa...
20 m in 14 days so 8 men in (20*14)/8 = 35 days
In 21 days 8 men complete (1/35)*21 = 3/5 work
Remaining work = 1 – 3/5 = 2/5
20 women do 1 work in 18 days so x women will do 2/5 work in 9 days
10*(2/5)*18 = x*1*9
In 21 days 8 men complete (1/35)*21 = 3/5 work
Remaining work = 1 – 3/5 = 2/5
20 women do 1 work in 18 days so x women will do 2/5 work in 9 days
10*(2/5)*18 = x*1*9
Most Upvoted Answer
20 men can complete a work in 14 days and 20 women can complete the sa...
20 m in 14 days so 8 men in (20*14)/8 = 35 days
In 21 days 8 men complete (1/35)*21 = 3/5 work
Remaining work = 1 – 3/5 = 2/5
20 women do 1 work in 18 days so x women will do 2/5 work in 9 days
10*(2/5)*18 = x*1*9
In 21 days 8 men complete (1/35)*21 = 3/5 work
Remaining work = 1 – 3/5 = 2/5
20 women do 1 work in 18 days so x women will do 2/5 work in 9 days
10*(2/5)*18 = x*1*9
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Community Answer
20 men can complete a work in 14 days and 20 women can complete the sa...
Given:
- 20 men can complete a work in 14 days.
- 20 women can complete the same work in 18 days.
- 8 men start the work and work for 21 days.
- They are then replaced by x women.
- The remaining work is to be completed by x women in 9 days.
To find:
The value of x, i.e., how many women should be employed to complete the remaining work in 9 days.
Let's solve this step by step:
Step 1: Find the amount of work done by 8 men in 21 days.
Since 20 men can complete the work in 14 days, the amount of work done by 1 man in 1 day is 1/ (20*14).
Therefore, the amount of work done by 8 men in 21 days is (1/ (20*14)) * 8 * 21.
Step 2: Find the amount of work remaining after 8 men worked for 21 days.
Since the work completed by 8 men in 21 days is subtracted from the total work, the remaining work is:
1 - [(1/ (20*14)) * 8 * 21].
Step 3: Find the amount of work done by x women in 9 days.
Since 20 women can complete the work in 18 days, the amount of work done by 1 woman in 1 day is 1/ (20*18).
Therefore, the amount of work done by x women in 9 days is (1/ (20*18)) * x * 9.
Step 4: Equate the remaining work to the work done by x women.
(1 - [(1/ (20*14)) * 8 * 21]) = (1/ (20*18)) * x * 9.
Step 5: Solve for x.
Simplifying the equation further, we get:
(1 - [(1/ (20*14)) * 8 * 21]) = (1/ (20*18)) * x * 9.
(1 - (1/ (20*14)) * 8 * 21) = (1/ (20*18)) * x * 9.
(1 - (3/10)) = (1/ (20*18)) * x * 9.
(7/10) = (1/ (20*18)) * x * 9.
(7/10) = (1/360) * x * 9.
x = (7/10) * 360 / 9.
x = 7 * 40.
x = 280.
Therefore, the number of women that should be employed to complete the remaining work in 9 days is 280.
Hence, the correct answer is option D) 16.
- 20 men can complete a work in 14 days.
- 20 women can complete the same work in 18 days.
- 8 men start the work and work for 21 days.
- They are then replaced by x women.
- The remaining work is to be completed by x women in 9 days.
To find:
The value of x, i.e., how many women should be employed to complete the remaining work in 9 days.
Let's solve this step by step:
Step 1: Find the amount of work done by 8 men in 21 days.
Since 20 men can complete the work in 14 days, the amount of work done by 1 man in 1 day is 1/ (20*14).
Therefore, the amount of work done by 8 men in 21 days is (1/ (20*14)) * 8 * 21.
Step 2: Find the amount of work remaining after 8 men worked for 21 days.
Since the work completed by 8 men in 21 days is subtracted from the total work, the remaining work is:
1 - [(1/ (20*14)) * 8 * 21].
Step 3: Find the amount of work done by x women in 9 days.
Since 20 women can complete the work in 18 days, the amount of work done by 1 woman in 1 day is 1/ (20*18).
Therefore, the amount of work done by x women in 9 days is (1/ (20*18)) * x * 9.
Step 4: Equate the remaining work to the work done by x women.
(1 - [(1/ (20*14)) * 8 * 21]) = (1/ (20*18)) * x * 9.
Step 5: Solve for x.
Simplifying the equation further, we get:
(1 - [(1/ (20*14)) * 8 * 21]) = (1/ (20*18)) * x * 9.
(1 - (1/ (20*14)) * 8 * 21) = (1/ (20*18)) * x * 9.
(1 - (3/10)) = (1/ (20*18)) * x * 9.
(7/10) = (1/ (20*18)) * x * 9.
(7/10) = (1/360) * x * 9.
x = (7/10) * 360 / 9.
x = 7 * 40.
x = 280.
Therefore, the number of women that should be employed to complete the remaining work in 9 days is 280.
Hence, the correct answer is option D) 16.
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