Question

Sameer has a bag full of marbles he takes out half of the marble present in the bag and put back one marble in the bag he repeats it 4 times in the end only 3 marble are left in the bag how many marbles were there originally

Answer 1

Let us start assuming there were total  x number of marbles in the bag

In the first step  :

He pick x/2 marbles  leaving  only x/2  in the bag  and then pick 1 more

So marble left at the end of first step =  ( x/2)  + 1

In second  step :  after taking half  only    (( x/2 ) +1)/2  are left  then he keep back 1

After second step marbles in the bag =   ( x/4  + 1/2)  + 1

In third  step : after taking half marbles   left are     ( x/4  + 1/2   + 1 )/2

After keeping  back one more   , marbles in the bag =  ( x/8 + 1/4  + 1/2)  + 1

In the fourth step :  after taking half , marble left are :  (( x/8 + 1/4+ 1/2) + 1) /2

After keeping back  1 more marble :      ( x/16  + 1/8 + 1/4 + 1/2)  +1

According to question the marbles left in the bag = 3

( x/16  + 1/8  + 1/4 + 1/2)  +1 = 3          Let's take Lcd  which is 16

( x +  2 + 4  + 8 +16)/16   = 3

( x+30 )/16 = 3

x+30 = 3*1

x= 48 -30 =  18

So the answer is 18 which means there were total of 18 marbles.