Question : Richa, Rita and Reena can independently complete a task in 8 hours, 12 hours and 24 hours, respectively. If they work together, how much time will they take to complete that task?
Option 1: 4 hours
Option 2: 5 hours
Option 3: 2 hours
Option 4: 3 hours
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Correct Answer: 4 hours
Solution :
Given: Richa can independently complete a task in 8 hours.
Rita can independently complete a task in 12 hours.
Reena can independently complete a task in 24 hours.
Let the total work be LCM of (8, 12, 24) = 24 units
Work = Efficiency × Time
⇒ Efficiency of Richa = $\frac{24}{8}$ = 3 units per hour
⇒ Efficiency of Rita = $\frac{24}{12}$ = 2 units per hour
⇒ Efficiency of Reena = $\frac{24}{24}$ = 1 unit per hour
If they work together, the time taken $=\frac{24}{3 + 2 + 1}=\frac{24}{6} =4$ hours
Hence, the correct answer is 4 hours.
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