1. A man passed one-sixth of his life in childhood, one-twelfth in youth and one-seventh as a bachelor. Five years after his marriage, a son was born who died four years before his father at half his father's final age. How many years did the man should have lived?
2. Find the smallest number which is fifty six less than its square?
Solution
1. Answer: 84
Explanation: If y is the total age of the man then y = y/6 + y/12 + y/7 + 5 + y/2 + 4. Solving this, we get y = 84.
2. Answer: -7
Explanation: If n is such a number, then n = n^2 - 56 and so n^2 - n - 56 = 0. This gives (n+7)(n-8) = 0. Since we want least value of n, n must be - 7.
