The Chocolate Problem!!
Ten Children are standing in a line. Each child has some chocolates with him. If the first child attempted to double the chocolates of all the others using his chocolates , he would fall short by 2 chocolates. If the second child took 2 chocolates from each of the remaining , he would have 3 chocolates less than what the first child initially had. Find the total number of chocolates with the third to the tenth child ??
The answer is 23.
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1 solution
Let C1,C2... C10 be child number
Given,
If the first child attempted to double the chocolates of all the others using his chocolates , he would fall short by 2 chocolates.
2(C2+C3+...+C10) = C1+2 Eqn-1
If the second child took 2 chocolates from each of the remaining , he would have 3 chocolates less than what the first child initially had.
C1-3 = 2C2+18
i.e 2C2 = C1-21 Eqn-2
From both the equations:-
C1-21+ 2(C3+C4+.....C10) = C1+2
2(C3+C4+.....+C10) = 23