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A contractor can complete a certain piece w of work in 9 days. He employed certain number of men, but 6 of them being absent from the very first day, the rest could finish the work in 15 days. How many men were originally employed?
- a)12
- b)15
- c)18
- d)24
Correct answer is option 'B'. Can you explain this answer?
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A contractor can complete a certain piece w of work in 9 days. He empl...
Given:
- A contractor can complete a piece of work in 9 days.
- He employed a certain number of men.
- 6 of them were absent from the first day.
- The rest could finish the work in 15 days.
To find: The original number of men employed.
Solution:
Let the original number of men employed be x.
From the given information, we know that:
- The contractor can complete the work in 9 days, so his one day work = 1/9.
- Let the efficiency of each man be y. So, the total efficiency of x men = xy.
- Work done by x men in 1 day = xy.
- Work done by x-6 men in 1 day = (x-6)y.
- In 15 days, work done by (x-6) men = 15(x-6)y.
- As the whole work is completed in 15 days by (x-6) men, their total work in 15 days = 1.
Using the above information, we can form the following equation:
1/9 = 15(x-6)y
=> xy = 15(x-6)y*9
=> x = 15*6*9/(15*9-y*6)
As we know that x is an integer, we can find the value of y that will make x an integer.
Factors of 6 are 1, 2, 3, 6.
Factors of 9 are 1, 3, 9.
Let's try substituting the values of y from the above factors and check which value of y gives an integer value of x.
For y = 1: x = 15*6*9/(15*9-1*6) = 15.23 (not an integer)
For y = 2: x = 15*6*9/(15*9-2*6) = 14.14 (not an integer)
For y = 3: x = 15*6*9/(15*9-3*6) = 12.81 (not an integer)
For y = 6: x = 15*6*9/(15*9-6*6) = 15 (an integer)
Therefore, the original number of men employed is x = 15.
Hence, the correct answer is option (B) 15.
- A contractor can complete a piece of work in 9 days.
- He employed a certain number of men.
- 6 of them were absent from the first day.
- The rest could finish the work in 15 days.
To find: The original number of men employed.
Solution:
Let the original number of men employed be x.
From the given information, we know that:
- The contractor can complete the work in 9 days, so his one day work = 1/9.
- Let the efficiency of each man be y. So, the total efficiency of x men = xy.
- Work done by x men in 1 day = xy.
- Work done by x-6 men in 1 day = (x-6)y.
- In 15 days, work done by (x-6) men = 15(x-6)y.
- As the whole work is completed in 15 days by (x-6) men, their total work in 15 days = 1.
Using the above information, we can form the following equation:
1/9 = 15(x-6)y
=> xy = 15(x-6)y*9
=> x = 15*6*9/(15*9-y*6)
As we know that x is an integer, we can find the value of y that will make x an integer.
Factors of 6 are 1, 2, 3, 6.
Factors of 9 are 1, 3, 9.
Let's try substituting the values of y from the above factors and check which value of y gives an integer value of x.
For y = 1: x = 15*6*9/(15*9-1*6) = 15.23 (not an integer)
For y = 2: x = 15*6*9/(15*9-2*6) = 14.14 (not an integer)
For y = 3: x = 15*6*9/(15*9-3*6) = 12.81 (not an integer)
For y = 6: x = 15*6*9/(15*9-6*6) = 15 (an integer)
Therefore, the original number of men employed is x = 15.
Hence, the correct answer is option (B) 15.
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A contractor can complete a certain piece w of work in 9 days. He employed certain number of men, but 6 of them being absent from the very first day, the rest could finish the work in 15 days. How many men were originally employed?a)12b)15c)18d)24Correct answer is option 'B'. Can you explain this answer?
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