Answer to Question #113497 in Algebra for Swapnil Bhardwaj

Question

Question.....
A men gone to atm but he forgot his A.T.M pin but he know something about his pin no.

1-The sum of all the no=12
2-the sum of no.2and no.3=8
3-no 1 is half of no.3
And no.1 and no.2 multiply to get no.4

Answer 1

If a, b, c, d are the pin numbers, then:

1) a + b + c + d = 12,

2) b + c = 8,

3) a = 0.5c,

4) a×b = d.

From 1, 2 and 4 we get:

a + 8 + ab = 12,

a + ab = 4,

a = 4/(1 + b).

From 3 we get:

4/(1 + b) = 0.5c,

c = 8/(1 + b).

From 2 we get:

$b + 8/(1 + b) = 8,$

$(b^2 + b + 8 - 8 - 8b)/(1 + b) = 0,$ (b is not equal -1),

$b^2 - 7b = 0,$

b = 0 or b = 7.

If b = 0, then c = 8 - 0 = 8, d = a×0 = 0, a = 0.5×8 = 4, so pin is 4080.

If b = 7, then c = 8 - 7 = 1, a = 0.5×1 = 0.5, which is impossible for pin, because it can consist of whole numbers lower than 10 only.

So, the only possible pin is 4080.