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But after 30 hours the destroyer was withdrawn.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After 30 h, destroyer was withdrawn, remainig work by P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.
