Question
Download Solution PDFAarif, Arun and Abraham can do a work in 12, 20 and 24 days, respectively. They all begin together. Arun leaves the work 3 days and Abraham 6 days before its completion. In how many days is the work finished?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Aarif, Arun and Abraham can do a work in 12, 20 and 24 days, respectively.
They all begin together. Arun leaves the work 3 days and Abraham 6 days before its completion.
Concept used:
Total work = Efficiency × Time
Calculation:
Let the total time taken by them be x days
Now,
LCM of 12, 20, and 24 = 120 i.e total work
So, efficiency of Aarif = 120/12
⇒ 10
Efficiency of Arun = 120/20
⇒ 6
Efficiency of Abraham = 120/24
⇒ 5
According to the question,
x × 10 + (x - 3) × 6 + (x - 6) × 5 = 120
⇒ 10x + 6x - 18 + 5x - 30 = 120
⇒ 21x = 120 + 48
⇒ 21x = 168
⇒ x = 8
∴ The required time is 8 days.
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