Question

In a computer game, a builder can build a wall in 20 hours while a destroyer can completely demolish such a wall in 40 hours. In the beginning, both builder and destroyer were set to work together on a basic level. But after 30 hours the destroyer was withdrawn. What was the total time taken to build the wall?

• A. 33 h 30 min
• B. 35 h
• C. 35 h 15 min
• D. 32 h 45 min

Answer 1

Answer:

B. 35 h

Solution: Given: A builder can build a wall in 20 hours while a destroyer can completely demolish such a wall in 40 hours. But after 30 hours the destroyer was withdrawn. Concept Used: Using the Least Common Multiple(LCM) Methods Calculation: Let the bulider can bulid the wall be P in 20 hours, and detsroyer demolish the wall be Q in 40 hours Total Work = LCM of (20 and 40) ⇒ 40 Effiiciency of P = 40/20 = 2 Efficiency of Q = 40/40 = 1 Both builder and destroyer were set to work together 30 h ⇒ 30 × (2 - 1) ⇒ 30 unit Remaining work = 40 - 30 = 10 unit After 30 h, destroyer was withdrawn, remainig work by P ⇒ 10/2 ⇒ 5 h Total time to complete the work ⇒ 30 + 5 = 35 h ∴ The total time taken to build the wall was 35 h.