Ramu had some money with him. He gave one rupee to beggar and he spent half of the remmaning money to by something fot himself. The next day also he gave one rupee to the beggar and spent half of the remaining to buy something for himself. This pattern continued for 6 days. On the sixth day, when he gave one rupee to the beggar, he found that there was no money left with him. Find out how much money did Ramu had in beginning.
Answers
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
This way
6th day->1
5-1+1+1->3
4-3+3+1>7
3->7+7+1=15
2->15+15+1=31
1->31+31+1=63
Answer: 48 rupees
Step-by-step explanation:
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)÷2)
After again giving Rupee. 1 to the beggar, money he had
= (x-1)÷2)-1 = (x-2)÷2
Amount Ramu spent on himself = (x-1)÷2
Money remaining after second day = ( x - 2 ) ÷ 4
Similarly,
Money remaining after third day = (x-4)÷8
Money remaining after fourth day = (x-8)÷16
Money remaining after fifth day = (x-16)÷32
Given, on sixth day, after giving Re. 1 to the beggar, he had no money left.
Money left with him after fifth day = Rupee. 1
∴ (x-16)÷32 = 1
⇒x-16 ÷ 32 = 1
⇒x - 16 = 1 x 32
⇒ x = 32 + 16
⇒ x = 48
Total money Ramu had in beginning = Rs. 48