X takes twice as much time as Y or thrice as much time as Z to finish a job. Working together, the trio can finish the job in 2 days. Y alone can do the work in ______.

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X takes twice as much time as Y or thrice as much time as Z to finish a job. Working together, the trio can finish the job in 2 days. Y alone can do the work in ______.

A6

B12

C18

D15

Answer:

A. 6

Read Explanation:

Solution: Given: Time taken by X = 2 × Time taken by Y Time taken by X = 3 × Time taken by Z Time to complete work together = 2 days Concept used: Efficiency to do a work is inversely proportional to time taken for the same. Total work = Time × Efficiency Calculation: According to the question, Time ratio, X : Y : Z = 6 : 3 : 2 So, Efficiency ratio = 1/6 : 1/3 : 1/2 Multiply each term by 6 ⇒ Efficiency ratio = 6/6 : 6/3 : 6/2 = 1 : 2 : 3 Combined efficiency = 6 units So, total work = 6 units × 2 = 12 units Efficiency 'of Y = 2 units So, time taken by Y alone to do the work = 12/2 = 6 days ∴ Y will finish the work alone in 6 days.

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