An apple seller is having some apples.?

Question

An apple seller is having some apples. He is selling half of the apple what he has plus half the apple to the first customer. In the same way he sells the remaining apple to 7 customers. After
selling to 7 customers he has no apple with him .No. of apples he have at the beginning?

Answer 1

Give a slightly clear statement.... It could be either 128 or 256.

Answer 2

All the above answers are wrong..

The answer is: 127 apples

No. of apples sold,
to first customer = (127/2) + (1/2) = 64 So,apples left = 63
to second customer = (63/2) + (1/2) = 64 So,apples left = 31
to third customer = (31/2) + (1/2) = 64 So,apples left = 15
to fourth customer = (15/2) + (1/2) = 64 So,apples left = 7
to fifth customer = (7/2) + (1/2) = 64 So,apples left = 3
to sixth customer = (3/2) + (1/2) = 64 So,apples left = 1
to seventh customer = (1/2) + (1/2) = 64 So,apples left = 0

Method Adopted:-

To the seventh customer, he sold half an apple + half the apples he already had. After this he had no apples.

He must have had 1 apple before selling to satisfy the above statement. i.e:- 1 - ( (1/2)*1 + (1/2) ) = 0

Proceeding similarly we arrive at the answer.

this can also be given by the equation, x suffix (n-1) = 2* x suffix (n) + 1

Alternate method:-

We can also assume that initially he had x apples. Number of apples sold to first customer = (x/2) + (1/2)

So number of apples left = x - (x/2 + 1/2)

we have to proceed similarly upto the seventh customer. We will get some terms which should be equated to zero to arrive at the answer.

This is a bit tedious and hence have avoided it. Interested people can try it.

Answer 3

If I understand correctly, the 1st customer gets three quarters of the total amount of apples,
the second customer gets three quarters of the apples left over from the first customer,
the third customer gets three quarters of the apples left over from the second customer,
and continues in a like manner but the seventh customer gets all the remaining apples from the sixth customer.

Let the total number of apples be N (number).

1st Customer gets = N * 3/4 = 3/4N = (3072 / 4096)N
2nd Customer gets = (1/4)N * 3/4 = (3/16)N = (768 / 4096)N
3rd Customer gets = (1/6)N * 3/4 = (3/64)N = (192 / 4096)N
4th Customer gets = (1/64)N * 3/4 = (3/256)N = (48 / 4096)N
5th Customer gets = (1/256)N * 3/4 = (3/1024)N = (12 / 4096)N
6th Customer gets = (1/1024)N * 3/4 = (3/4096)N = (3 / 4096)N
7th Customer gets = (1/1024)N (remainder).

Because of insufficient information the exact number of Apples is unknown. However, the calculation above show the fraction ratios.

The smallest fraction we have is 1 / 4096.
This implies the smallest number of Apples there must be is 4096 apples. If the apple seller started off with 4096 Apples, then the customers would receive:

1st Customer gets 3072 Apples.
2nd Customer gets 768 Apples.
3rd Customer gets 192 Apples.
4th Customer gets 48 Apples.
5th Customer gets 12 Apples.
6th Customer gets 3 Apples.
7th Customer gets 1 Apple.

If the Apple seller did not start off with 4096 Apples, then he would have started off with a multiple of this number, that is:
4096 x 2 or,
4096 x 3 or,
4096 x 4 or,
and etc.

Answer 4

3½

7 customers times ½ an apple per customer.

Answer 5

448 maybe
ie 7*2 then= 6times
why? you tell us

Answer 6

question is not clear is it 14?

Answer 7

applesauce