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20 men can complete a piece of work in 14 days. 7 men started the work and after 20 days, 7 more men joined the work. In how many days the remaining work will be completed?
- a)18 days
- b)20 days
- c)8 days
- d)12 days
- e)10 days
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
20 men can complete a piece of work in 14 days. 7 men started the work...
Let (7+7) complete remaining work in x days.
So 20*14 = 7*20 + 14*x
x = 10 days
So 20*14 = 7*20 + 14*x
x = 10 days
Most Upvoted Answer
20 men can complete a piece of work in 14 days. 7 men started the work...
Given data:
Number of men required to complete the work = 20
Time taken by 20 men to complete the work = 14 days
7 men started the work and worked for 20 days
After 20 days, 7 more men joined the work
Let's calculate the work done by 7 men in 20 days
Work done by 7 men in 1 day = 1/ (20*20/7) = 7/400
Work done by 7 men in 20 days = (7/400) * 20 = 7/20
Let's calculate the total work done by 7 men in 20 days
Total work done by 7 men in 20 days = (7/20) * 7 = 49/20
Remaining work = 1 - 49/20 = 31/20
Let's calculate the work done by 7 men and 7 more men in 1 day
Work done by 7 men and 7 more men in 1 day = (7+7)/ (20*14) = 1/20
Now, let's calculate the number of days required to complete the remaining work
Let the number of days required to complete the remaining work be x
(7+7) men will work for (20+x) days to complete the remaining work
Work done by (7+7) men in (20+x) days = (7+7) * (1/20) * (20+x) = 14(20+x)/20 = 7(20+x)/10
Total work done by 14 men in (20+x) days = 7/20 + 7(20+x)/10
As per the given data, the total work done by 14 men in (20+x) days should be equal to the remaining work
Therefore, we can equate the above equation to 31/20 and solve for x
7/20 + 7(20+x)/10 = 31/20
7(20+x)/10 = 31/20 - 7/20
7(20+x)/10 = 24/20
20+x = 24*10/7
20+x = 34.2857
x = 34.2857 - 20
x = 14.2857 ≈ 14
Therefore, the remaining work will be completed in 14 days.
Hence, option E is the correct answer.
Number of men required to complete the work = 20
Time taken by 20 men to complete the work = 14 days
7 men started the work and worked for 20 days
After 20 days, 7 more men joined the work
Let's calculate the work done by 7 men in 20 days
Work done by 7 men in 1 day = 1/ (20*20/7) = 7/400
Work done by 7 men in 20 days = (7/400) * 20 = 7/20
Let's calculate the total work done by 7 men in 20 days
Total work done by 7 men in 20 days = (7/20) * 7 = 49/20
Remaining work = 1 - 49/20 = 31/20
Let's calculate the work done by 7 men and 7 more men in 1 day
Work done by 7 men and 7 more men in 1 day = (7+7)/ (20*14) = 1/20
Now, let's calculate the number of days required to complete the remaining work
Let the number of days required to complete the remaining work be x
(7+7) men will work for (20+x) days to complete the remaining work
Work done by (7+7) men in (20+x) days = (7+7) * (1/20) * (20+x) = 14(20+x)/20 = 7(20+x)/10
Total work done by 14 men in (20+x) days = 7/20 + 7(20+x)/10
As per the given data, the total work done by 14 men in (20+x) days should be equal to the remaining work
Therefore, we can equate the above equation to 31/20 and solve for x
7/20 + 7(20+x)/10 = 31/20
7(20+x)/10 = 31/20 - 7/20
7(20+x)/10 = 24/20
20+x = 24*10/7
20+x = 34.2857
x = 34.2857 - 20
x = 14.2857 ≈ 14
Therefore, the remaining work will be completed in 14 days.
Hence, option E is the correct answer.
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Community Answer
20 men can complete a piece of work in 14 days. 7 men started the work...
Let (7+7) complete remaining work in x days.
So 20*14 = 7*20 + 14*x
x = 10 days
So 20*14 = 7*20 + 14*x
x = 10 days
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