Three people together build a house in 75 days when they work together, while two of them work to build the house and one person does the work of destroying the house. If two people , who make the house , they can together build the house in 37.5 days , then in how many days can the person , who destroys the house alone demolish the house ?

Let the work rates be a, b (builders) and -c (destroyer, negative sign). Together: a + b - c = 1/75. Two builders alone: a + b = 1/37.5 = 2/75. Substituting: 2/75 - c = 1/75, so c = 1/75. This means the destroyer alone would take 75 days to demolish the house. The key insight is that the destroyer's work rate subtracts from the builders' combined effort.