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Find the time taken by 8 men, 4 women and 6 kids together to complete the piece of work.
Statement I: 6 men and 4 women together can complete the work in 12 days and 1 man and 8 women together can complete the work in 17 days.
Statement II: The ratio of efficiencies of a woman and a kid is 5 : 2.
Statement I: 6 men and 4 women together can complete the work in 12 days and 1 man and 8 women together can complete the work in 17 days.
Statement II: The ratio of efficiencies of a woman and a kid is 5 : 2.
- a)Both Statements I and II together are not sufficient to answer the question.
- b)Statements I and II together are required to answer the question.
- c)Either statement I or statement II alone is sufficient to answer the question.
- d)Statement II alone is sufficient to answer the questio
- e)Statement I alone is sufficient to answer the question.
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Find the time taken by 8 men, 4 women and 6 kids together to complete ...
Statement I:
6 men and 4 women together can complete the work in 12 days and 1 man and 8 women together can complete the work in 17 days.
Suppose the efficiencies of man and woman are ‘m’ and ‘w’ respectively.
So,
(6 × m + 4 × w) × 12 = (1 × m + 8 × w) × 17
⇒ 72m + 48w = 17m + 136w
⇒ 55m = 88w
⇒ m : w = 8 : 5
So, ratio of efficiencies of a man and a woman = 8 : 5
Combining statement II:
Ratio of efficiencies of a woman and a kid = 5 : 2
Ratio of efficiencies of a man, a woman and a kid = 8 : 5 : 2
Suppose the work done by men, women and kid be 8x, 5x and 2x respectively
Now,
Suppose the time taken by 8 men, 4 women and 6 kids together is T days
(6 × 8x + 4 × 5x) × 12 = (8 × 8x + 4 × 5x + 6 × 2x) × T
⇒ (48x + 20x) × 12 = (64x + 20x + 12x) × T
⇒ 68x × 12 = 96x × T
⇒ T = 8.5
Time taken by 8 men, 4 women and 6 kids together = 8.5 days
∴ Statements I and II together are required to answer the question.
6 men and 4 women together can complete the work in 12 days and 1 man and 8 women together can complete the work in 17 days.
Suppose the efficiencies of man and woman are ‘m’ and ‘w’ respectively.
So,
(6 × m + 4 × w) × 12 = (1 × m + 8 × w) × 17
⇒ 72m + 48w = 17m + 136w
⇒ 55m = 88w
⇒ m : w = 8 : 5
So, ratio of efficiencies of a man and a woman = 8 : 5
Combining statement II:
Ratio of efficiencies of a woman and a kid = 5 : 2
Ratio of efficiencies of a man, a woman and a kid = 8 : 5 : 2
Suppose the work done by men, women and kid be 8x, 5x and 2x respectively
Now,
Suppose the time taken by 8 men, 4 women and 6 kids together is T days
(6 × 8x + 4 × 5x) × 12 = (8 × 8x + 4 × 5x + 6 × 2x) × T
⇒ (48x + 20x) × 12 = (64x + 20x + 12x) × T
⇒ 68x × 12 = 96x × T
⇒ T = 8.5
Time taken by 8 men, 4 women and 6 kids together = 8.5 days
∴ Statements I and II together are required to answer the question.
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Find the time taken by 8 men, 4 women and 6 kids together to complete ...
Understanding the Problem
To find the time taken by 8 men, 4 women, and 6 kids to complete the work, we need to determine their combined efficiency using the given statements.
Statement I Analysis
- Efficiency of Men and Women:
- 6 men and 4 women can complete the work in 12 days.
- Therefore, their combined work rate is 1/12 of the work per day.
- Efficiency Calculation:
- Let the efficiency of 1 man be M and that of 1 woman be W.
- From this statement, we can form the equation:
- 6M + 4W = 1/12 (Work done per day)
- Efficiency of 1 Man and 8 Women:
- 1 man and 8 women can complete the work in 17 days.
- This leads to another equation:
- M + 8W = 1/17 (Work done per day)
Statement II Analysis
- Efficiency Ratio:
- The ratio of efficiencies of a woman to a kid is 5:2.
- Let the efficiency of a woman be 5x and that of a kid be 2x.
Combining Statements I and II
- Solving the Equations:
- With both statements, we can express all variables (M, W, and K where K is the efficiency of a kid) in terms of x.
- Combine the two equations from Statement I and the efficiency ratios from Statement II.
Conclusion
- Sufficiency of Information:
- Both statements together provide enough information to calculate the efficiencies of men, women, and kids.
- This allows us to find the total efficiency of 8 men, 4 women, and 6 kids.
Therefore, the correct answer is option 'B': Statements I and II together are required to answer the question.
To find the time taken by 8 men, 4 women, and 6 kids to complete the work, we need to determine their combined efficiency using the given statements.
Statement I Analysis
- Efficiency of Men and Women:
- 6 men and 4 women can complete the work in 12 days.
- Therefore, their combined work rate is 1/12 of the work per day.
- Efficiency Calculation:
- Let the efficiency of 1 man be M and that of 1 woman be W.
- From this statement, we can form the equation:
- 6M + 4W = 1/12 (Work done per day)
- Efficiency of 1 Man and 8 Women:
- 1 man and 8 women can complete the work in 17 days.
- This leads to another equation:
- M + 8W = 1/17 (Work done per day)
Statement II Analysis
- Efficiency Ratio:
- The ratio of efficiencies of a woman to a kid is 5:2.
- Let the efficiency of a woman be 5x and that of a kid be 2x.
Combining Statements I and II
- Solving the Equations:
- With both statements, we can express all variables (M, W, and K where K is the efficiency of a kid) in terms of x.
- Combine the two equations from Statement I and the efficiency ratios from Statement II.
Conclusion
- Sufficiency of Information:
- Both statements together provide enough information to calculate the efficiencies of men, women, and kids.
- This allows us to find the total efficiency of 8 men, 4 women, and 6 kids.
Therefore, the correct answer is option 'B': Statements I and II together are required to answer the question.
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Find the time taken by 8 men, 4 women and 6 kids together to complete the piece of work.Statement I: 6 men and 4 women together can complete the work in 12 days and 1 man and 8 women together can complete the work in 17 days.Statement II: The ratio of efficiencies of a woman and a kid is 5 : 2.a)Both Statements I and II together are not sufficient to answer the question.b)Statements I and II together are required to answer the question.c)Either statement I or statement II alone is sufficient to answer the question.d)Statement II alone is sufficient to answer the questioe)Statement I alone is sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer?
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Solutions for Find the time taken by 8 men, 4 women and 6 kids together to complete the piece of work.Statement I: 6 men and 4 women together can complete the work in 12 days and 1 man and 8 women together can complete the work in 17 days.Statement II: The ratio of efficiencies of a woman and a kid is 5 : 2.a)Both Statements I and II together are not sufficient to answer the question.b)Statements I and II together are required to answer the question.c)Either statement I or statement II alone is sufficient to answer the question.d)Statement II alone is sufficient to answer the questioe)Statement I alone is sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Banking Exams.
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ample number of questions to practice Find the time taken by 8 men, 4 women and 6 kids together to complete the piece of work.Statement I: 6 men and 4 women together can complete the work in 12 days and 1 man and 8 women together can complete the work in 17 days.Statement II: The ratio of efficiencies of a woman and a kid is 5 : 2.a)Both Statements I and II together are not sufficient to answer the question.b)Statements I and II together are required to answer the question.c)Either statement I or statement II alone is sufficient to answer the question.d)Statement II alone is sufficient to answer the questioe)Statement I alone is sufficient to answer the question.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Banking Exams tests.
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