**Roses Puzzle**I have a number of roses for sale. The first buyer bought half of my roses then I gave him additional one for free. The second buyer bought half of the remaining roses then I gave him additional one also for free. The third buyer also bought half of the remaining roses then I gave him additional one also for free, this time all of my roses has been sold out.

How many roses do I have?

How many roses do I have?

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14

ReplyDeleteBuyer 3

ReplyDeletesay seller had x no of roses and (x/2) sold and 1 free

(x/2)+1 = 2

hence x = 2

Buyer 2

say seller had y no of roses and (y/2) sold and 1 free

y=(y/2)+1+x

2y=y+2+2(2)

y=6

Buyer 3

say seller had z no of rose and (z/2) sold 1 free

z=(z/2)+1+y

2z=z+2+2y

2z = z+2+12

z=14

so total rose with seller were 14

;)

-dinesh

it is 14.

ReplyDelete14

ReplyDeleteThe Third buyer purchased half of remainig roses, plus one free rose, and this leave zero rose witht he seller. This is only possible when, while third buyer was purchasing, there were only two rose.

ReplyDeleteSo,

Third buyer purchased 1 rose + got 1 free and stock before his purchase was 2 (A).

Stock before Second buyer purchased will be ((A) + 1 ) x 2, i.e. 6 (B)

Stock before First buyer puchased will be ((B) + 1) x 2, i.e. 14.

There were 14 flower in the beginning

Let there was n roses then

ReplyDelete(n/2+1)+(n/4+1/2)+(n/8+1/4)=n

then we get n=14 Ans.