Question

A man entered an orchard that had 7 guards and he picked some apples.When he left, he gave the first guard half his apples and 1 more. To the second guard he gave half his remaining apples and 1 more. He did the same to each of the remaining five guards and left the orchard with only 1 Apple. How many apples did he gather in all

Answer 1

we know that

gate 7 starts with x, ends up with 1

x - ((1/2)x + 1) = 1

x - (1/2)x - 1 = 1

(1/2)x = 2

x = 4

gate 6 starts with x, ends up with 4

x - ((1/2)x + 1) = 4

x - (1/2)x - 1 = 4

(1/2)x = 5

x = 10

gate 5 starts with x, ends up with 10

(1/2)x = 11

x = 22

gate 4 starts with x, ends up with 22

(1/2)x = 23

x = 46

gate 3 starts with x, ends up with 46

(1/2)x = 47

x = 94

gate 2

(1/2)x = 95

x = 190

gate 1

(1/2)x = 191

x = 382

The answer is He started with 382 apples