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Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how many days will the same piece of work be done by 1 man, 1 woman and 1 boy? can anyone help me out
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Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how...
Problem Statement: Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how many days will the same piece of work be done by 1 man, 1 woman, and 1 boy?
Analysis:
To solve this problem, we need to determine the number of days required for 1 man, 1 woman, and 1 boy to complete the work. We are given the information that:
- Two men can complete the work in 66 days.
- 1 woman can complete the work in 66 days.
- 3 boys can complete the work in 66 days.
Solution:
Let's assume that the efficiency of work done by a man, woman, and boy is represented by M, W, and B respectively.
Since two men can complete the work in 66 days, we can write the equation as:
2M = 66 days
Similarly, for 1 woman and 3 boys, we have:
W = 66 days
3B = 66 days
Now, we need to find the equation for 1 man, 1 woman, and 1 boy working together.
Let's assume the time required for them to complete the work is represented by T.
The combined efficiency of 1 man, 1 woman, and 1 boy can be represented as:
M + W + B = 1/T
Since we know the values of M, W, and B in terms of days, we can substitute them in the equation:
(1/2) + (1/66) + (1/3) = 1/T
Simplifying this equation, we get:
(33 + 1 + 22)/66 = 1/T
(56/66) = 1/T
56T = 66
T = 66/56
T = 1.18 days (approx)
Therefore, 1 man, 1 woman, and 1 boy working together can complete the work in approximately 1.18 days.
Analysis:
To solve this problem, we need to determine the number of days required for 1 man, 1 woman, and 1 boy to complete the work. We are given the information that:
- Two men can complete the work in 66 days.
- 1 woman can complete the work in 66 days.
- 3 boys can complete the work in 66 days.
Solution:
Let's assume that the efficiency of work done by a man, woman, and boy is represented by M, W, and B respectively.
Since two men can complete the work in 66 days, we can write the equation as:
2M = 66 days
Similarly, for 1 woman and 3 boys, we have:
W = 66 days
3B = 66 days
Now, we need to find the equation for 1 man, 1 woman, and 1 boy working together.
Let's assume the time required for them to complete the work is represented by T.
The combined efficiency of 1 man, 1 woman, and 1 boy can be represented as:
M + W + B = 1/T
Since we know the values of M, W, and B in terms of days, we can substitute them in the equation:
(1/2) + (1/66) + (1/3) = 1/T
Simplifying this equation, we get:
(33 + 1 + 22)/66 = 1/T
(56/66) = 1/T
56T = 66
T = 66/56
T = 1.18 days (approx)
Therefore, 1 man, 1 woman, and 1 boy working together can complete the work in approximately 1.18 days.
Community Answer
Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how...
one man or 2 women or 3 boys can finish a job in 66 days. the formula to use is:R * P * T = QR = rate per person.P = number of personsT = timeQ = quantity of work. set Q = 1 piece of work.set T = 66set P = the number of personsyou will want to solve for R which will give you the rate per person. for the man:R * P * T = Q becomes:R * 1 * 66 = 1divide both sides of this equation by 66 and you get:R * 1 = 1/66divide both sides of this equation by 1 to get:R = 1/66one man can finish 1/66 of the job in 1 day. for the women:R * P * T = Q becomes:R * 2 * 66 = 1divide both sides of this equation by 66 and you get:R * 2 = 1/66divide both sides of this equation by 2 to get:R = 1/132one woman can finish 1/132 of the job in 1 day. for the boys:R * P * T = Q becomes:R * 3 * 66 = 1divide both sides of this equation by 66 and you get:R * 3 = 1/66divide both sides of this equation by 3 to get:R = 1/198one boy can finish 1/198 of the job in 1 day. the question is:how many days will one man, one woman and one boy together take to finish the same work? the rate of one man is 1/66the rate of one woman is 1/132the rate of 1 boy is 1/198 working together their rates are additive. you get: R * P * T = 1Since P is equal to 1 all around, this formula becomes:R * T = 1The R in this case is the overall rate of the 3 people working together.we get:R = (1/66 + 1/132 + 1/198) which is equivalent to:R = (6/396 + 3/396 + 2/396) which is equivalent to:R = 11/396 R * T = 1 becomes:11/396 * T = 1divide both sidesof this eqution by (11/396) and you get:T = 1 / (11/396) = 1 * (396/11) = 396/11 = 36 days. 1 man and 1 woman and 1 boy, working together, can complete the work in 36 days. the man will have completed 1/66 * 36 = 36/66 of the work in 36 days.the woman will have completed 1/132 * 36 = 36/132 of the work in 36 days.the boy will have completed 1/198 * 36 = 36/198 of the work in 36 days. add these up together and you should get 1.36/66 + 36/132 + 56/198 is equivalent to:(36*6 + 36*3 + 36*2) / 396 which is equivalent to:(216 + 108 + 72) / 396 which is equivalent to:396/396 which is equivalent to 1. solution is correct.answer is 36 days.
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Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how many days will the same piece of work be done by 1 man, 1 woman and 1 boy? can anyone help me out
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Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how many days will the same piece of work be done by 1 man, 1 woman and 1 boy? can anyone help me out for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how many days will the same piece of work be done by 1 man, 1 woman and 1 boy? can anyone help me out covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how many days will the same piece of work be done by 1 man, 1 woman and 1 boy? can anyone help me out.
Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how many days will the same piece of work be done by 1 man, 1 woman and 1 boy? can anyone help me out for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how many days will the same piece of work be done by 1 man, 1 woman and 1 boy? can anyone help me out covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two men or 1 woman or 3 boys can do a piece of work in 66 days. In how many days will the same piece of work be done by 1 man, 1 woman and 1 boy? can anyone help me out.
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