Puzzle-8

The Singhs recently were visited by their favourite uncle, who had landed from America. The parents displayed all the five kids. First in line was Bunny and then can Geet. When the uncle asked how old they were, Mr. Singh said that the boy was exactly twice as old as the girl. Then in walked Harpreet, who told that the combined age of Geet and herself was twice that of Bunny. Then the next kid, Chatur came running in and all excited (possibly on account of the fact that he might receive some gifts), and the mother of the kids remarked that the combined ages of the two boys were exactly twice the combined ages of the two girls. The Uncle has barely absorbed all these facts when Jaspreet entered the room and announced, “Uncle you have actually arrived on my 21st birthday”. To this fact, Mr. Singh finally added: “The combined ages of my three girls is exactly equal to twice the combined ages of my two boys”. What were the ages of the kids, according to these facts provided to the uncle of the kids?

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The ages were as follows: Bunny, 3½ years; Geet, 1¾ year; Harpreet, 5¼ years; Chatur, 10½; years; and Jaspreet, 21 years.

Explanation: With the given information, we can build the some equations. By reading the puzzle carefully, we can establish that there are two boys and three girls: Boys : Bunny , Chatur Girls : Geet , Harpreet, Jaspreet

Now from the information given in the question, we form the equations to find the ages of these children:

B=2G…………………..I H+G=2B ………………II C+B =2(G+H)…………III J= 21…………………..IV (GIVEN ) J+G+H =2(C+B)………….V

From these equations, we find the respective ages of the kids.

First for the value of H: We have: B=2G Put this in the equation II We have: H+G=3B H+G=2(2G) H+G=4G H=4G-G H=3G………………………………VI

We also know J+G+H=2(C+B) J+2B=2C+2B( from eq.II)

As we know the age of J is 21 so 21=2C C=21/2…………………………….VII

Now from eq.III and II C+B=2(2B) C+B=4B C=3B Now put value of c from VII B becomes 21/6=7/2 B=7/2………………………………..VIII Now let’s revisit the first equation now We have: B=2G 7/2=2G G=7/4……………………………….IX

From equation II we have: H+G=2B H=2(2G) – G H= 3G H=3X7/4=21/4………………………X

Thus, solving these equations, we arrive at the ages of all the kids: J = Jaspreet = 21 years C= Chatur = 21/2 years B= Bunny = 7/2 years G = Geet = 7/4 years H= Harpreet = 21/4 years