A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?
Started 3 months ago by Shashank in
Explanatory Answer
These questions work with a backward approach.
The 5 child gets half of what was remaining after 4 child + 1, this essentially means the 5 child
got 2 toffees.
Now the gentleman had 2 toffees after giving half of what was remaining after child 3 + 1, this
means he had 2*(2+1) = 6 left after giving the third child. Hence the 4-child got
0.5*6 + 1 = 4 and 2 were left for 5-child.
Similarly, after giving second child he had 2*(6+1) = 14 toffees
After giving first child he had 2*(14+1) = 30 toffees
Initially he had 2*(30+1) = 62 toffees
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