Question

While 3 watchman were guarding a orchard ,a thief slipped in and stole some apples .on his way out he met the three watchman one after another.he had to give half the apples plus two to each watchman in turn .in this way he managed to flee away with one apple .how many apples had he stolen originally . Answer please with full solution and statment

Answer 1

Apples left with theif = 1
he had to give half the apples plus two to each watchman in turn,
Let apples with the thief before meeting 3rd thief = x
1/2 *x +2 = apples given to third watchman
= x - 1
1/2 *x + 2 = x - 1
1/2* x - x = - 1 - 2
x - 1/2 * x = 3
(2x - x) /2 =3
x = 6
Let apples with the thief before meeting 2nd watchman be y
1/2*y +2 = apples given to 2nd watchman
= y - 6
y - 1/2 * y = 6 + 2
(2y - 2)/2 = 8
y = 16
apples with the thief before meeting 2nd theif = 16
Let apples with the thief before meeting 1st watchman = z
z /2 + 2 = apples given to 1st watch man = z - 16
z / 2 + 2 = z - 16
z - z/2 = 16 + 2
(2z - z) /2 = 18
z = 36
Total apples stolen = 36
Apples given to 1st watchman =20
Apples given to 2nd watchman = 10
Apples given to 3rd watchman = 5

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