Question

1. A maharaja owned a mango tree that had very sweet, abundant fruit.
People would come from miles around to
pick the fruit. So the maharaja decided to
protect the tree by erecting a series of
seven concentric fences around it. Each
fence had a gate with a guard. To get to
the tree a person would have had to pass through seven gates and pass
seven guards. One day, a man approached the guard at the
first gate and said, "If you let me pass, when I come back I'll
bring you some mangoes. I will give you half of the
mangoes I have, but you must give me one back." For
example, if he brings back 10 mangoes, he'll give five to the
guard and the guard will give one back. The guard let the
man in through the gate, and the man proceeded to make
the same deal with the other six guards.
The question is: How many mangoes did the man have
to get to pass back through the seven gates, giving half
to each guard and the guard giving one back and still
having 5 mangoes for him in the end.​

Answer 1

Answer:

386

Step-by-step explanation:

let say man had 2x mangoes before any gate then he gave x mangoes to guard and guard return one mango

so after crossing gate he will have

2x - x + 1 = x + 1 mangoes

x + 1 = 5

so x = 4

2x = 8

x + 1 = y y is manogoes after gate

x = y-1

2x = 2 (y-1)

after 7th gate = 5

after 6th gate = before 7th gate = 2(5-1) = 8

after 5th gate = before 6th gate = 2(8-1) = 14

after 4th gate = before 5th gate = 2(14-1) = 26

after 3rd gate = before 4th gate = 2(26-1) = 50

after 2nd gate = before 3rd gate = 2(50-1) = 98

after 1st gate = before 2nd gate = 2(98-1) = 194

before 1st gate = 2(194-1) = 386