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21 men can complete a piece of work in 16 days while 10 women can complete the same piece of work in 26 days. 24 men start working and are replaced by 13 women after 7 days. In how many days will 13 women finish the remaining work?
- a)11 days
- b)14 days
- c)13 days
- d)10 days
- e)15 days
Correct answer is option 'D'. Can you explain this answer?
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21 men can complete a piece of work in 16 days while 10 women can comp...
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21 men can complete a piece of work in 16 days while 10 women can comp...
Given:
21 men can complete a piece of work in 16 days
10 women can complete the same piece of work in 26 days
To find:
In how many days will 13 women finish the remaining work?
Solution:
Let's first calculate the total work to be done.
Let the total work be W.
We know that,
21 men can complete the work in 16 days
⇒ 1 man can complete the work in 21 * 16 days
⇒ 1 man can complete the work in 336 days
Also, 10 women can complete the work in 26 days
⇒ 1 woman can complete the work in 10 * 26 days
⇒ 1 woman can complete the work in 260 days
Let's assume that there are M men and W women required to complete the work.
According to the given conditions,
M men can complete the work in 16 days
⇒ 1 man can complete the work in 16 * M days
⇒ Work done by M men in 1 day = 1/(16*M)
W women can complete the work in (260/W) days
⇒ 1 woman can complete the work in (260/W) * W days
⇒ Work done by 1 woman in 1 day = 1/260
24 men start working and are replaced by 13 women after 7 days.
Work done by 24 men in 7 days = 24 * 7/(16*24) = 7/16
Remaining work = 1 - 7/16 = 9/16
Let's assume that the men work for M more days and then women work for W days to complete the remaining work.
So, we have the following two equations:
(1) Work done by M men in M days + Work done by W women in W days = 9/16
(2) Work done by 24 men in 7 days + Work done by M men in M days = 7/16
Substituting the value of work done by M men in equation (2), we get:
Work done by 24 men in 7 days + 1/(16*M) * M = 7/16
⇒ 7/16 - 7/16 = -1/(16*M)
⇒ -1/(16*M) = -7/16
⇒ M = 7
Substituting the value of M in equation (2), we get:
Work done by 24 men in 7 days + Work done by 7 men in 7 days = 7/16
⇒ 7/16 + 7/(16*3) = 7/16
⇒ Work done by 7 men in 7 days = 0
Substituting the value of M in equation (1), we get:
Work done by 7 men in 7 days + Work done by W women in W days = 9/16
⇒ Work done by W women in W days = 9/16
⇒ W = 10
So, 13 women will complete the remaining work in W days.
⇒ Work done by 1 woman in 1 day = 1/260
⇒ Work done by 13 women
21 men can complete a piece of work in 16 days
10 women can complete the same piece of work in 26 days
To find:
In how many days will 13 women finish the remaining work?
Solution:
Let's first calculate the total work to be done.
Let the total work be W.
We know that,
21 men can complete the work in 16 days
⇒ 1 man can complete the work in 21 * 16 days
⇒ 1 man can complete the work in 336 days
Also, 10 women can complete the work in 26 days
⇒ 1 woman can complete the work in 10 * 26 days
⇒ 1 woman can complete the work in 260 days
Let's assume that there are M men and W women required to complete the work.
According to the given conditions,
M men can complete the work in 16 days
⇒ 1 man can complete the work in 16 * M days
⇒ Work done by M men in 1 day = 1/(16*M)
W women can complete the work in (260/W) days
⇒ 1 woman can complete the work in (260/W) * W days
⇒ Work done by 1 woman in 1 day = 1/260
24 men start working and are replaced by 13 women after 7 days.
Work done by 24 men in 7 days = 24 * 7/(16*24) = 7/16
Remaining work = 1 - 7/16 = 9/16
Let's assume that the men work for M more days and then women work for W days to complete the remaining work.
So, we have the following two equations:
(1) Work done by M men in M days + Work done by W women in W days = 9/16
(2) Work done by 24 men in 7 days + Work done by M men in M days = 7/16
Substituting the value of work done by M men in equation (2), we get:
Work done by 24 men in 7 days + 1/(16*M) * M = 7/16
⇒ 7/16 - 7/16 = -1/(16*M)
⇒ -1/(16*M) = -7/16
⇒ M = 7
Substituting the value of M in equation (2), we get:
Work done by 24 men in 7 days + Work done by 7 men in 7 days = 7/16
⇒ 7/16 + 7/(16*3) = 7/16
⇒ Work done by 7 men in 7 days = 0
Substituting the value of M in equation (1), we get:
Work done by 7 men in 7 days + Work done by W women in W days = 9/16
⇒ Work done by W women in W days = 9/16
⇒ W = 10
So, 13 women will complete the remaining work in W days.
⇒ Work done by 1 woman in 1 day = 1/260
⇒ Work done by 13 women
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21 men can complete a piece of work in 16 days while 10 women can complete the same piece of work in 26 days. 24 men start working and are replaced by 13 women after 7 days. In how many days will 13 women finish the remaining work?a)11 daysb)14 daysc)13 daysd)10 dayse)15 daysCorrect answer is option 'D'. Can you explain this answer?
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21 men can complete a piece of work in 16 days while 10 women can complete the same piece of work in 26 days. 24 men start working and are replaced by 13 women after 7 days. In how many days will 13 women finish the remaining work?a)11 daysb)14 daysc)13 daysd)10 dayse)15 daysCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about 21 men can complete a piece of work in 16 days while 10 women can complete the same piece of work in 26 days. 24 men start working and are replaced by 13 women after 7 days. In how many days will 13 women finish the remaining work?a)11 daysb)14 daysc)13 daysd)10 dayse)15 daysCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 21 men can complete a piece of work in 16 days while 10 women can complete the same piece of work in 26 days. 24 men start working and are replaced by 13 women after 7 days. In how many days will 13 women finish the remaining work?a)11 daysb)14 daysc)13 daysd)10 dayse)15 daysCorrect answer is option 'D'. Can you explain this answer?.
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