Love of chocolate

Number Theory Level pending

Priyanka visited a famous monument called “holyghar” located near Himalayas. It was a round structure consisting of 100 steps in spiral stairway to reach top. From top you can have overview of natural beauty surrounding that place. Priyanka thought of reaching the top. She also carried a lot of chocolates with her for kids. In the process of climbing up, with each step a chocolate falls from her bag. When she reaches top, she donates half of the chocolates left with her to small kids. Again, in the process of climbing down a chocolate falls down with each step.

She repeats the same process at five holyghars and now she is left with no chocolates. Can you find out the total number of chocolates she had with her initially?

The answer is 9300.

1 solution

Chandrakant Pandey
Dec 5, 2016

Let us begin from the end. We have fifth holyghar to consider first.

Priyanka climbed down hundred steps so after donating she must be left with 100 chocolates. Now she donates half of total chocolates so before donating she must be having 200 chocolates.

Now she loses 100 chocolates while climbing up so in total she must be having 300 chocolates before climbing fifth holyghar.

Now the same procedure is followed for fourth holyghar. So before climbing fourth she must be having (300+100)*2+100 chocolates which amounts to 900.

Before climbing third, she must be having (900+100)*2+100 which amounts to 2100. Now before climbing second she must be having 4500 chocolates.

At last , before climbing first she must be having 9300 chocolates. So initially she had in total 9300 chocolates.

Love of chocolate

The answer is 9300.

1 solution

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