8 men and 12 boys can finish a piece of work in10 days while 6 men and 8 boys finish
it in14 days. Find the time taken by one man alone and by one boy alone to finish the
work.
Answers
Given:
✭ Time taken by 8 men and 12 boys to complete the work =10 days
✭ Time taken by 6 men and 8 boys to complete the work = 14 days
To Find:
◈ Time taken by one man and one boy alone to complete the work?
Solution:
Let the time taken by a man alone to complete the work be x days
Let the time taken by a boy alone to complete the work be y days.
By given,
⪼ 8/x + 12/y =1/10---(1)
In the second case,
⪼ 6/x + 8/y = 1/14---(2)
Let 1/x =p, 1/y = q
Hence equation 1 and 2 changes to
➢ 8p + 12q = 1/10---(3)
➢ 6p + 8q = 1/14---(4)
Multiply equation 3 by 3 and 4 by 4
➠24p + 36q = 3/10
➠24p + 32q = 4/14
Solving by elimination method,
»» 4q = 3/10 - 4/14
»» 4q = 3/10 - 2/7
»» 4q = 21/70 - 20/70
»» 4q = 1/70
»» q = 1/280
But we know that 1/y = q, y = 1/q = y=280
Hence time taken by one boy alone is 180 days
Substitute the value of q in the above equation
➝ 24p + 36/280 = 3/10
➝ 24p + 9/70 = 3/10
➝ 24p = 3/10 - 9/70
➝ 24p = 21/70 - 9/70
➝ 24p = 12/70
➝ p = 12/1680
➝ p =1/140
But we know that 1/x = p, x = 1/p , x = 140
Hence time taken by one man alone is 140 days
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Answer:
Please see the attachment ⬆️ Hope it helps
