Working together, Ash
assigned task in 20 d
alone and completed hal
the work a
fether, Asha and Sudha can complete an
sk in 20 days. However, if Asha worked
completed half the work and then Sudha
ver the task and completes the second half
the task, the task will be completed in 45 days.
How long will Asha take to complete the task if she
worked alone? Assume that Sudha is more efficient
than Asha.
Answers
Asha will take 60 days to complete the task if she worked alone
Step-by-step explanation:
Let say Asha can complete the work in A Days
& Sudha can complete the work in S days
Sudha is more efficient than Asha. => S < A
Asha and Sudha can complete together in 20 Days
=> 1/A + 1/S = 1/20
=> S + A = SA/20
=> 20S + 20A = SA
A/2 + S/2 = 45
=> A + S = 90
=> S = 90 - A
=> 20(90 - A) + 20A = (90- A)A
=> 1800 - 20A + 20A = 90A - A²
=> A² - 90A + 1800 = 0
=> A² - 30A - 60A + 1800 = 0
=> A(A - 30) - 60(A - 30) = 0
=> (A - 30)(A - 60) = 0
=> A = 30 or 60
S = 60 or 30
as Sudha is more efficient than Asha.
=> Asha will take 60 days to complete the task if she worked alone
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