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Question
A takes 10days less than B to Finish a piece of work , If both A and B work together , they can finish the work in 12 days. Find the time taken by B to finish the work.
Solution
Let B take 'c' days to finish the work. Hence, A will take 'c - 1 O' days.
⇒ Work done by B in One day = `1/"c"` , whereas work done by A in one day = `(1/("c" - 10))`
⇒ Work done by A and B combined in one day = `1/"c" + 1/("c" - 10) = ("c" - 10 + "c")/("c"^2 - 10"c")`
⇒ c2 - 10c = 24c -120
⇒ c2 -34c + 120 = 0
⇒ c2 -30c - 4c + 120 = 0
⇒ c (c -30) - 4(c - 30) = 0
⇒ (c - 30)(c - 4) = 0.
It can't be 4 as they together complete in 12 days and hence has to be more than that.
Hence no. of days taken by B to finish the work = 30
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