shwetha takes 6 days less than the number of days taken by ankita to complete a piece of work.If both shwetha and ankita together can complete the same work is 4 days.In how many days will Ankita alone complete the work?
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Answered by
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Work completed by ankita in X days = 1
work completed by ankita in 1 day = 1/X
Work completed by shweta in X - 6 days (as because shweta takes 6 days less to complete a work) = 1
work completed by shweta in 1 day = 1 / X-6
work completed by both ankita and shweta in (1/X + 1/X-6) = ?
NOW AS PER QUESTION ;
work completed by both ankita and shweta in 4 (1/X + 1/X-6) = 1
4 [X-6 +X / X(X-6)] = 1
4 [2X -6 / X^2 - 6X ] = 1
8X - 24 / X^2 - 6X = 1
by the method of cross multiplication , we get ;
8X - 24 = X^2 -6X
transferring all the terms at one side ,
X^2 - 14X + 24 = 0
by the method of MIDDLE TERM SPLIT , we get ;
X^2 - 12X - 2X + 24 = 0
X(X-12) -2(X-12) = 0
(X-2)(X-12) = 0
therefore X will be equal to 2 or 12 , but as in case of shweta , the number of days i which 1 work completed will be negative , we will go with our second tion , that is 12.
therefore 1 work completed by ankita in = 12 days
shweta in = 12 - 6 days = 6 days
HOPE IT HELPS . MARK AS BRAINLIEST , AND DON'T FORGET TO FOLLOW.
work completed by ankita in 1 day = 1/X
Work completed by shweta in X - 6 days (as because shweta takes 6 days less to complete a work) = 1
work completed by shweta in 1 day = 1 / X-6
work completed by both ankita and shweta in (1/X + 1/X-6) = ?
NOW AS PER QUESTION ;
work completed by both ankita and shweta in 4 (1/X + 1/X-6) = 1
4 [X-6 +X / X(X-6)] = 1
4 [2X -6 / X^2 - 6X ] = 1
8X - 24 / X^2 - 6X = 1
by the method of cross multiplication , we get ;
8X - 24 = X^2 -6X
transferring all the terms at one side ,
X^2 - 14X + 24 = 0
by the method of MIDDLE TERM SPLIT , we get ;
X^2 - 12X - 2X + 24 = 0
X(X-12) -2(X-12) = 0
(X-2)(X-12) = 0
therefore X will be equal to 2 or 12 , but as in case of shweta , the number of days i which 1 work completed will be negative , we will go with our second tion , that is 12.
therefore 1 work completed by ankita in = 12 days
shweta in = 12 - 6 days = 6 days
HOPE IT HELPS . MARK AS BRAINLIEST , AND DON'T FORGET TO FOLLOW.
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Answered by
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Answer:
Step-by-step explanation:
1/x-6
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