The king's task surprises the end. The key is in 1 relationship

Mathematical puzzles can combine logical reasoning with a short communicative that seems irrelevant at first glance. In this puzzle appears a king and simple fractions. Everything looks innocent, but it leads to 1 precise result, if you correctly read the dependencies.
In this kind of puzzle, memory to dates is not important, but the ability to compare parts to the whole. The content contains fractions of what part of life the king ruled was. The most crucial presumption is that the minute of taking the throne remains the same, so erstwhile life shortens or prolongs, the time of government changes precisely the same. This allows you to easy convert the description into 2 simple equations. Only then comes the time to calculate, and these are more orderly than the game suggests.

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Mathematical puzzles can spin your head. past checks if you can think in proportions
Imagine that you only know 2 sentences about a king's life, and you gotta infer the remainder from proportion. If a king had died 5 years earlier, he would have reigned for a 4th of his life. If he had lived 9 years longer, he would have reigned for half his life. Your task is specific: calculate how many years he lived and how many years he ruled.


How many years did he live and how many years did the king rule?


In this mathematical riddle, it is worth immediately clarifying the meaning of both variants, due to the fact that it is the easiest thing to do here. We don't decision the minute of the throne, we decision the minute of death, erstwhile earlier, erstwhile later. This means that the number of years of reign changes by precisely 5 or 9 years, as does the number of years of life. There are no hidden changes here, specified as early in power or a longer childhood, due to the fact that that is not given. This allows you to think of 2 pairs of numbers that vary by constant value and then compare them in fraction form. In the first option, part, or rule, is simply a 4th of the total, or life. In the second option, the same part in the fresh version represents half of the total. Many people confuse these proportions and effort to compare a 4th to half without referring them to circumstantial years, and this leads nowhere. Here you gotta stick to a simple pattern: first a description, then a record, only at the end of the bill. erstwhile the evidence is correct, the full problem becomes amazingly clear.


The solution to the mathematical puzzle does not require Olympic cunning. Just compose 2 equations and see if the consequence matches both conditions
Let's say the life expectancy of x, and the duration of y. In the variant of the first certain king lives x minus 5 years and reigns y minus 5 years. The condition is that in this variant, regulation is simply a 4th of life, so you compose the equation, y minus 5 is equal to a 4th of x minus 5. In the second variant of a certain king lives x plus 9 years and reigns y plus 9 years. So you compose y plus 9 is equal to 1 second times x plus 9. These are 2 independent conditions that describe the same unknown x and y.


Now, you're going to kind out both equations to express x over y in each equation. From the first equation after simple transformation you get x is equal to 4y minus 15. The another is x is equal to 2y plus 9. If both of these are about the same life, you compare them to each another and you get 4y minus 15 is equal to 2y plus 9. You subtract 2y on both sides and then 2y is equal to 24. You divide by 2 and you get y is equal to 12. Then you substitute it for a more comfortable formula, like to x is equal to 2y plus 9, and you get x is equal to 33.


In the end, it's worth doing control, due to the fact that in math puzzles, it's the fastest way to catch an mistake in the record. If a king lived 33 years and reigned 12 years, he would have been 28 years old and 7 years old before his death. 1 4th of 28 is precisely 7, so the first condition is met. If he had lived 9 years longer, he would have lived 42 years and 21 years. Half of 42 is 21, so the second condition agrees. This closes the full communicative and shows that the numbers match both versions simultaneously.
One more thing is worth clarifying, for sometimes there are doubts about those who solve specified tasks. The solution is only due to the fact that you have 2 equations with 2 unknowns and both conditions are consistent, so they lead to 1 pair of values. If conditions were excluded, there could be no solution, and if they were dependent, there could be infinitely many. Here the situation is clear: equations are not the same transformation, so they indicate 1 result. The answer is that 1 king lived 33 years and reigned 12 years.