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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