Question
Download Solution PDFRani and Adya, working separately, can finish a task in 12 days and 16 days, respectively. They work in stretches of one day alternately. If Rani starts working first, then the task will be completed in
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Rani's work days = 12 days
Adya's work days = 16 days
Rani starts the work.
Formula used:
Work done in 1 day = 1 / total days
Total work = LCM of individual work days
Calculations:
LCM of 12 and 16 = 48
Rani's 1 day work = 48 / 12 = 4 units
Adya's 1 day work = 48 / 16 = 3 units
Work done in 2 days (Rani + Adya) = 4 + 3 = 7 units
Number of 2 day cycles to complete nearly 48 units = 48 / 7 = 6.85
6 full cycles of 2 days = 6 × 2 = 12 days
Work done in 12 days = 6 × 7 = 42 units
Remaining work = 48 - 42 = 6 units
On the 13th day, Rani works and completes 4 units.
Remaining work = 6 - 4 = 2 units
On the 14th day, Adya works and completes 2 units.
Adya completes 2 units in 2/3 of a day, since she does 3 units in one day.
Total days = 12 + 1 + 2/3 = 13 + 2/3 = 13 + (2/3) days
Total days = 13 and 2/3 days.
∴ The task will be completed in 13 and 2/3 days.
Last updated on Jul 17, 2025
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