Deepak takes 6 days less than the time taken by suresh to finish a piece of work if both deepak and suresh together can finish it in 4 days find the time taken by suresh to finish the work
Answers
Suresh takes 10 days
Answer:
The time taken by suresh to complete the given work is 12 days and the time taken by deepak to complete the work is 6 days.
Step-by-step explanation:
Let the time taken by suresh to complete the work be X days
Therefore time taken by deepak will be X - 6 days
According to the given condition
1/X + 1/X-6 = 1/4
X - 6 + X / X² - 6X = 1/4
8X - 24 = X² - 6X
X² - 14X + 24 = 0
We will solve this by middle term splitting
The factors are -12X and -2X
Substitute these values instead of the middle term and you get
X² - 12X - 2X +24 = 0
Take common between first two and second two terms
X (X - 12) - 2 (X-12) = 0
(X - 2) (X - 12) = 0
Therefore X = 2 or X = 12
But if X i.e. time taken by suresh is 2 then the time taken by deepak will be X - 6 = 2 - 6 = -4 days
But days cannot be negative therefore X = 12 and X - 6 = 12 - 6 = 6
So the time taken by suresh to complete the given work is 12 days and the time taken by deepak to complete the work is 6 days.
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