A boy puts money in his piggybank everyday. He puts some money on the 1st day. He puts double the amount on the 2nd day. On 10th day his piggybank becomes full, on which day did his piggybank become half?
Answers
Given : A boy puts money in his piggybank everyday. He puts some money on the 1st day. He puts double the amount on the 2nd day. On 10th day his piggybank becomes full,
To Find : on which day did his piggybank become half?
Solution:
On 1st Day = A
on 2nd day = 2A = A* 2¹
On 3rd Day = 4A = A * 2²
..
--
On 10th day = A * 2⁹ = 512A
Total = A + 2A + 4A +...................+ 2⁹A
Sₙ = A(2¹⁰ - 1)/(2 - 1)
Sₙ = 1023A
Full = 1023A
Filled on last day = 512A
so before last day (9th Day) = 1023A - 512A = 511A
1023/2 = 511.5 A
Hence Almost half on 9th Day
Piggy Bank become half on 9th days
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