Question
'P' and 'Q' together can complete a task in 20 days. 'P'
alone would take 12 days fewer than 'Q' to finish it. How many days would 'Q' take to do the work alone?Solution
ATQ,
Let the number of days 'Q' takes = x
Then, time taken by 'P' = x – 12
According to the question:
(1/20) = (1/x) + (1/(x – 12))
⇒ (1/20) × x × (x – 12) = x + (x – 12)
⇒ x² – 12x = 20(2x – 12)
⇒ x² – 12x = 40x – 240
⇒ x² – 52x + 240 = 0
⇒ x² – 48x – 4x + 240 = 0
⇒ x(x – 48) – 4(x – 48) = 0
⇒ (x – 48)(x – 4) = 0
So, x = 48 or x = 4
Since at x = 4, P’s time becomes negative,
x = 48
Therefore, Q can do the work alone in 48 days.
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