Question : Rahul can complete his work in 7 days and Raj can complete the work in 4 days. How many total days will they take to complete the work together?
Option 1: $\frac{14}{11}$ days
Option 2: $\frac{15}{11}$ days
Option 3: $\frac{28}{13}$ days
Option 4: $\frac{28}{11}$ days
Correct Answer: $\frac{28}{11}$ days
Solution :
Given: Rahul can complete his work in 7 days and Raj can complete the work in 4 days.
Total work = Efficiency × Time
The total work = LCM(7, 4) = 28 units
Rahul's efficiency = $\frac{28}{7}$ = 4 units per day
Raj's efficiency = $\frac{28}{4}$ = 7 units per day
Total efficiency of Rahul and Raj = 7 + 4 = 11 units per day
The total number of days they take to complete the work together = $\frac{28}{11}$ days
Hence, the correct answer is $\frac{28}{11}$ days.
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