Question
Download Solution PDFX, Yand Z can do a work in 24 days. 5 days and 12 days, respectively. In how many days can they do the same work if they work together?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Time taken by X to do the work = 24 days.
Time taken by Y to do the work = 5 days.
Time taken by Z to do the work = 12 days.
Formula used:
Work rate = 1 / Time taken
Combined work rate = Work rate of X + Work rate of Y + Work rate of Z
Time taken when working together = 1 / Combined work rate
Calculation:
Work rate of X = 1 / 24
Work rate of Y = 1 / 5
Work rate of Z = 1 / 12
Combined work rate = (1 / 24) + (1 / 5) + (1 / 12)
To add the fractions, find the LCM of 24, 5, and 12, which is 120.
⇒ Combined work rate = (5 / 120) + (24 / 120) + (10 / 120)
⇒ Combined work rate = (5 + 24 + 10) / 120
⇒ Combined work rate = 39 / 120
Time taken when working together = 1 / (39 / 120)
⇒ Time taken when working together = 120 / 39
⇒ Time taken when working together = 3(1/13) days
∴ The correct answer is option 3.
Last updated on Jun 26, 2025
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