Question

Q . Ram had some money with him . He gave one to a begger and he spent half of remainning money to buy somethig for himself . The next day he gave one rupee to the begger and spent half of the remaining to buy domething for himself . This pattern continued for 6 days . On sixth day , when he gave one rupee to begger , he found that there was no money left with him . Find how much money left with him . Find out how much money did Ram had in the brginning ?

Answer 1

Answer :

Let Ram have total money in beginning = x
And as given He gave one to a beggar , Than he left with total money = x - 1
and he spent half of remaining money to buy something for himself , So
He spent on himself = $\frac{x-1}{2}$ .
And Remaining money after one day = ( x - 1 ) - $\frac{x-1}{2}$ = $\frac{x-1}{2}$

And Again he gave one rupee to beggar , So money lest with him = $\frac{x-1}{2}$ - 1 = $\frac{x-3}{2}$
And again he spent half of remaining money to buy something for himself , So

He spent on himself = $\frac{x-3}{4}$ .
And Remaining money after second day = $\frac{x-3}{2}$ - $\frac{x-3}{4}$ = $\frac{x-3}{4}$
So,
We can see the pattern of remaining money, And can say

Remaining money after Third day = $\frac{x-7}{8}$
And
Remaining money after forth day = $\frac{x-15}{16}$
And
Remaining money after fifth day = $\frac{x-31}{32}$
And given : On sixth day , when he gave one rupee to beggar , he found that there was no money left with him .
So,
Money left with him after fifth day = 1 rupee .
So,
$$\begin{gathered} \Rightarrow \frac{x-31}{32}=1 \\ \Rightarrow x-31=32 \\ \Rightarrow x=63 \end{gathered}$$

So,
As given no money left with him after sixth day so, he have no money after sixth day .

And
Ram have total money in beginning = Rs 63 ( Ans )