Question
"A" and "B" collaborate to complete a project in 18
days. If "A" can finish the project 15 days faster than "B" when working solo, how long would it take "B" to complete the project alone?Solution
Let the time taken by 'B' to finish the work be 'x' days. So, time taken by 'A' to finish the work = 'x - 15' days ATQ; (1/18) = (1/x) + {1/(x - 15) } Or, (1/18) X (x - 15) X x = (x - 15) + x Or, x2Â - 15x = 18 X (2x - 15) Or, x2Â - 15x = 36x - 270 Or, x2Â - 51x + 270 = 0 Or, x2Â - 45x - 6x + 270 = 0 Or, x(x - 45) - 6(x - 45) = 0 Or, (x - 45) (x - 6) = 0 So, x = 45 or x = 6 Since, at x = 6, time taken by 'A' to finish the work would become negative So, x = 45 So, 'B' would finish the work alone in 45 days. Hence, option a.
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