A and b together can complete a work in 14 2/5 days while b and c together can complete the same work in 10 2/7 days a alone starts work and afyer 8 days b replaced him b did the work for next 12 days and the remaining work is completed by c in next 5 days then find time taken by a b c together to complete that worl if c work with 50% of his usual efficiency
Answers
Given : A and b together can complete a work in 14 2/5 days while b and c together can complete the same work in 10 2/7 day
To find : time taken by a b c together to complete that work if c work with 50% of his usual efficiency
Solution:
A Alone complete work in A days
B alone complete work in B days
C alone complete work in C days
1/a + 1/b = 5/72
1/b + 1/c = 7/72
8/a + 12/b + 5/c = 1
8 ( 5/72 - 1/b) + 12/b + 5(7/72 - 1/b) = 1
=> 40/72 - 8/b + 12/b + 35/72 - 5/b = 1
=> -1/b = 1 - 75/72
=> -1/b = -3/72
=> b = 24
1/a + 1/b = 5/72
=> 1/a + 3/72 = 5/72
=> 1/a = 2/72
=> a = 36
1/b + 1/c = 7/72
=> 3/72 + 1/c = 7/72
=> 1/c = 4/72
=> c = 18
1/a = 1/36
1/b = 1/24
1/c = 1/18
c's efficiency half
=> 1/c = 1/36
1/36 + 1/24 + 1/36
= (2 + 3 + 2)/72
= 72/7
= 10 2/7 Days
time taken by a b c together to complete that work 10 2/7 Days if c work with 50% of his usual efficiency
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