Question
Download Solution PDFRajeshwar can do a piece of work in 12 days, Vikram in 6 days and Tiger in 15 days. They all start the work together, but Rajeshwar leaves after 2 days and Vikram leaves 3 days before the work is completed. In how many days is the work completed?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Rajeshwar's work time = 12 days
Vikram's work time = 6 days
Tiger's work time = 15 days
Formula used:
Total work = LCM of individual work times
Work done = Efficiency × Time
Calculations:
LCM of 12, 6, and 15 = 60 (Total work)
Rajeshwar's efficiency = 60/12 = 5 units/day
Vikram's efficiency = 60/6 = 10 units/day
Tiger's efficiency = 60/15 = 4 units/day
Rajeshwar worked for 2 days, so work done by him = 5 × 2 = 10 units
Let the total number of days the work was completed be 'x' days.
Vikram worked for (x - 3) days.
Tiger worked for x days.
Total work done = Rajeshwar's work + Vikram's work + Tiger's work
60 = 10 + 10(x - 3) + 4x
⇒ 60 = 10 + 10x - 30 + 4x
⇒ 60 = 14x - 20
⇒ 80 = 14x
⇒ x = 80/14 = 40/7 = \(5 \frac{5}{7}\) days.
∴ The work is completed in 40/7 days, or \(5 \frac{5}{7}\) days.
Last updated on Jun 30, 2025
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