Maths Puzzles

 A man left legacies to his 3 sons and a hospital. The total amount of his legacy was $1320. If he had left the hospital legacy to his first son, he would have received as much as other two sons together. If he had left the hospital legacy to his second son, he would have received twice as much as the other two sons together. If he had left the hospital legacy to his third son, he would have received thrice as much as the other two sons together. Find the amount of each legacy.  Solution: Let the legacies of first, second and third sons be x,y and z respectively. Let h be the legacy of the hospital. Given x+y+z+h = 1320 x+h = y+z y+h = 2* (x+z) z+h = 3*(x+y) Replacing h with 1320-x-y-z, we get the equations as x+1320-x-y-z = y+z y+1320-x-y-z = 2*(x+z) z+1320-x-y-z = 3*(x+y) Simplifying and solving we get x = 55, y = 275 and z = 385. And h = 605

 Here was the question   "When I got to the station this morning," said Harold Tompkins, at his club, "I found I was short of cash. I spent just one-half of what I had on my railway ticket, and then bought a nickel's worth of candy. When I got to the terminus I spent half of what I had left and ten cents for a news-paper. Then I spent half of the remainder on a bus and gave fifteen cents to that old beggar outside the club. Consequently I arrive here with this single nickel. How much did I start out with?" Solution : Let us use a bottom up approach here.  Mr. Tompkins (funny name!) had a nickel when he reached his destination.  Prior to that he gave 15 cents to a beggar . Before giving money to beggar he had 15+5 = 20 cents. Before that, he spent half his money for bus ticket. Which means  20 = half of what he had Money he had before buying bus ticket = 2*20 = 40 cents  At the time of reaching bus terminal, he had spent half of what he had+10 cents to purc

 "When I got to the station this morning," said Harold Tompkins, at his club, "I found I was short of cash. I spent just one-half of what I had on my railway ticket, and then bought a nickel's worth of candy. When I got to the terminus I spent half of what I had left and ten cents for a news-paper. Then I spent half of the remainder on a bus and gave fifteen cents to that old beggar outside the club. Consequently I arrive here with this single nickel. How much did I start out with?" (By the way 1 nickel is 5 cents and 100 cents is 1 dollar. I googled it)   Find the solution in this post.

  By the way, gold ingot is a gold bar. I googled. This is quite a simple puzzle.  Solution :  Let us say the weight of of ingot is x kg.  On one side of scale is 1 ingot = x kg On the other side is 1/2 ingot and 3/4kg weight = x/2+3/4 As they balance,   x = x/2 + 3/4 Transferring x/2 to LHS, we get  x - x/2 = 3/4  x/2 = 3/4  x = 2* 3/4 = 1.5 kg  

Puzzle 1 : When asked his age, Jack tells that "In 2 years I will be twice as old as I was six years ago" . How old is Jack now? Puzzle 2: James  was  asked how old he is.  James said: “Five years ago my Dad was five times older than me, but now he is only three times older!” How old is James and how old is his father? Solutions :  1. If Jack's age is x, then    x+2 = 2*(x-6)    x+2 = 2x-12 2+12= 2x-x  x = 14 Jack is 14 years old now. 2. If James's age is x and his father's age is y, x*3 = y and  (x-5)*5 = y-5 Substituting y with 3x in the above equation, we get 5x - 25 = (3x) - 5  2x = 25 - 5 = 20 x = 10 and y = 30 So James is 10 years old and his father is 30 years old.