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2 men and 3 boys together can do a piece of work in 8 days.the same work is done in 6 days by 3 men and 2 boys together. how long would 1 boy alone and 1 men alone take to complete the work?
Verified Answer
2 men and 3 boys together can do a piece of work in 8 days.the same wo...
Let the number of days taken by a man and a boy be x and y respectively.
Therefore, work done by a man in 1 day =
Work done by a boy in 1 day =
According to the questions,
8[(2/x)(3/y)]=1
(2/x)(3/y)=1/8 (1)
6[(3/x)(2/y)] = 1
(3/x)(2/y)=1/6 (2)
Putting in these equations, we obtain
2p +3q = 1/8
16p +24q = 1 (3)
3p + 2q = 1/6
18p +12q = 1 (4)
p = (1-12q )/18 (5)
apply the (5) on (3)
16-192q + 432q = 18
q = 1/120 = 1/ y
y = 120
p = (1-12q)/18
= 1/20 = 1/x
x = 20
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Most Upvoted Answer
2 men and 3 boys together can do a piece of work in 8 days.the same wo...
Given Information:
- 2 men and 3 boys can complete a piece of work in 8 days.
- 3 men and 2 boys can complete the same work in 6 days.
Let's assume:
- The efficiency of 1 man in a day = M
- The efficiency of 1 boy in a day = B
Calculating the work:
- The work done by 2 men and 3 boys in 1 day = 1/8
- The work done by 3 men and 2 boys in 1 day = 1/6
Equations:
- 2M + 3B = 1/8 ...(1)
- 3M + 2B = 1/6 ...(2)
Solving the equations:
Multiplying equation (1) by 3 and equation (2) by 2, we get:
- 6M + 9B = 3/8 ...(3)
- 6M + 4B = 1/3 ...(4)
Subtracting equation (4) from equation (3), we get:
- 6B - 4B = 3/8 - 1/3
- 2B = 9/24 - 8/24
- 2B = 1/24
- B = 1/48
Substituting the value of B in equation (1), we get:
- 2M + 3(1/48) = 1/8
- 2M + 1/16 = 1/8
- 2M = 1/8 - 1/16
- 2M = 2/16 - 1/16
- 2M = 1/16
- M = 1/32
Calculating time taken by 1 boy alone:
- Work done by 1 boy in 1 day = 1/48
- Time taken by 1 boy alone to complete the work = 1 / (1/48) = 48 days
Calculating time taken by 1 man alone:
- Work done by 1 man in 1 day = 1/32
- Time taken by 1 man alone to complete the work = 1 / (1/32) = 32 days
Summary:
- 1 boy alone would take 48 days to complete the work.
- 1 man alone would take 32 days to complete the work.
- 2 men and 3 boys can complete a piece of work in 8 days.
- 3 men and 2 boys can complete the same work in 6 days.
Let's assume:
- The efficiency of 1 man in a day = M
- The efficiency of 1 boy in a day = B
Calculating the work:
- The work done by 2 men and 3 boys in 1 day = 1/8
- The work done by 3 men and 2 boys in 1 day = 1/6
Equations:
- 2M + 3B = 1/8 ...(1)
- 3M + 2B = 1/6 ...(2)
Solving the equations:
Multiplying equation (1) by 3 and equation (2) by 2, we get:
- 6M + 9B = 3/8 ...(3)
- 6M + 4B = 1/3 ...(4)
Subtracting equation (4) from equation (3), we get:
- 6B - 4B = 3/8 - 1/3
- 2B = 9/24 - 8/24
- 2B = 1/24
- B = 1/48
Substituting the value of B in equation (1), we get:
- 2M + 3(1/48) = 1/8
- 2M + 1/16 = 1/8
- 2M = 1/8 - 1/16
- 2M = 2/16 - 1/16
- 2M = 1/16
- M = 1/32
Calculating time taken by 1 boy alone:
- Work done by 1 boy in 1 day = 1/48
- Time taken by 1 boy alone to complete the work = 1 / (1/48) = 48 days
Calculating time taken by 1 man alone:
- Work done by 1 man in 1 day = 1/32
- Time taken by 1 man alone to complete the work = 1 / (1/32) = 32 days
Summary:
- 1 boy alone would take 48 days to complete the work.
- 1 man alone would take 32 days to complete the work.
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2 men and 3 boys together can do a piece of work in 8 days.the same work is done in 6 days by 3 men and 2 boys together. how long would 1 boy alone and 1 men alone take to complete the work?
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2 men and 3 boys together can do a piece of work in 8 days.the same work is done in 6 days by 3 men and 2 boys together. how long would 1 boy alone and 1 men alone take to complete the work? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 2 men and 3 boys together can do a piece of work in 8 days.the same work is done in 6 days by 3 men and 2 boys together. how long would 1 boy alone and 1 men alone take to complete the work? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 men and 3 boys together can do a piece of work in 8 days.the same work is done in 6 days by 3 men and 2 boys together. how long would 1 boy alone and 1 men alone take to complete the work?.
2 men and 3 boys together can do a piece of work in 8 days.the same work is done in 6 days by 3 men and 2 boys together. how long would 1 boy alone and 1 men alone take to complete the work? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 2 men and 3 boys together can do a piece of work in 8 days.the same work is done in 6 days by 3 men and 2 boys together. how long would 1 boy alone and 1 men alone take to complete the work? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 men and 3 boys together can do a piece of work in 8 days.the same work is done in 6 days by 3 men and 2 boys together. how long would 1 boy alone and 1 men alone take to complete the work?.
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