Question : Aarif, Arun, and Abraham can do work in 12, 20, and 24 days, respectively. They all begin together. Arun leaves the work 3 days and Abraham 4 days before its completion. In how many days is the work finished?
Option 1: 8
Option 2: 10
Option 3: 11
Option 4: 9
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Correct Answer: 8
Solution :
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 = $\frac{120}{12}$ = 10
Efficiency of Arun = $\frac{120}{20}$ = 6
Efficiency of Abraham = $\frac{120}{24}$ = 5
According to the question,
$x\times 10 + (x - 3) \times 6 + (x - 6) \times 5 = 120$
⇒ $10x + 6x - 18 + 5x - 30 = 120$
⇒ $21x = 120 + 48$
⇒ $21x = 168$
⇒ $x = 8$
Hence, the correct answer is 8.
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