RAMU had money. he gave one rupee to a beggar and he spent half of theremaining mony to buy for himself. the next day alsohe gave 0ne rupeeto the beggar and spent half of the remaining to buy himself.thispattern continued for 6 days. onthe sixthday. when he gave one rupeeto the beggar, he found that there was no money left with him. findout how much money did ramu had inthe beginning
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Let the amount of money Ramu had in beginning = x
After giving Re. 1 to the beggar, amount of money he had = x-1
Amount Ramu spent on himself = (x-1)÷2
Money remaining after first day = (x-1)-((x-1)÷2) = (x-1)÷2
After again giving Re. 1 to the beggar, money he had = ((x-1)÷2)-1 - (x-3)÷2
Amount Ramu spent on himself = (x-3)÷4
Money remaining after second day = ((x-3)÷2)-((x-3)÷4) = (x-3)÷4
Similarly,Money remaining after third day = (x-7)÷8
Money remaining after fourth day = (x-15)÷16
Money remaining after fifth day = (x-31)÷32
Given, on sixth day, after giving Re. 1 to the beggar, he had no money left.
Money left with him after fifth day = Re. 1
∴ (x-31)÷32 = 1
⇒x-31 = 32
⇒x = 63
Total money Ramu had in beginning = Rs. 63
After giving Re. 1 to the beggar, amount of money he had = x-1
Amount Ramu spent on himself = (x-1)÷2
Money remaining after first day = (x-1)-((x-1)÷2) = (x-1)÷2
After again giving Re. 1 to the beggar, money he had = ((x-1)÷2)-1 - (x-3)÷2
Amount Ramu spent on himself = (x-3)÷4
Money remaining after second day = ((x-3)÷2)-((x-3)÷4) = (x-3)÷4
Similarly,Money remaining after third day = (x-7)÷8
Money remaining after fourth day = (x-15)÷16
Money remaining after fifth day = (x-31)÷32
Given, on sixth day, after giving Re. 1 to the beggar, he had no money left.
Money left with him after fifth day = Re. 1
∴ (x-31)÷32 = 1
⇒x-31 = 32
⇒x = 63
Total money Ramu had in beginning = Rs. 63
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