Question

Robert takes twice as much time as Tom and thrice as much time as George to complete a work. If working together, they can complete it in 23 hours, then find the time that Tom will take to complete the work.

• A. 46 hours
• B. 69 hours
• C. 11 hours
• D. 39 hours

Answer 1

Answer:

B. 69 hours

Solution: Given: Robert takes to complete a work = 2 × Tom's work = 3 × George's work Working together they can complete a work = 23 hours Calculation: ⇒ Let George take to complete a work = 2y ⇒ Tom takes to complete a work = 3y ⇒ Robert take to complete a work = 6y Total work = LCM of (2y + 3y + 6y) = 6y Efficiency of all three = 3 + 2 + 1 = 6 Time taken by all of them to complete the work = total work/efficiency ⇒ 6y/6 = y ⇒ Working together they can complete a work = 23 hours y = 23 ⇒ Now Tom will take to complete the work = 3y = 23 × 3 = 69 hours ∴The correct answer is 69 hours.