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 Dollars and Cents (Posted on 2012-08-13)
This is a generalization of Rupees and Paise.

Stan entered a departmental store with A dollars and B cents. When he exited the store, he had B/p dollars and A cents, where B/p is an integer. It was observed that when Stan came out, he had precisely 1/p times the money he had when he came in.

Given that each of A, B and p is a positive integer, with 2 ≤ p ≤ 99, determine the values of p for which this is possible. What values of p generate more than one solution?

 See The Solution Submitted by K Sengupta No Rating

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 computer solution | Comment 3 of 5 |

DEFDBL A-Z
CLS
FOR p = 2 TO 99
FOR a = 1 TO 99
FOR b = p TO 99 STEP p
IF ((b / p) * 100 + a) * p = a * 100 + b THEN
PRINT p, a; b, b / p; a
END IF
NEXT b
NEXT a
NEXT p

finds all the solutions:

entered        left
with         with
p              a   b       b/p  a

2             99  98        49  99

4             33  32        8  33
4             66  64        16  66
4             99  96        24  99

5             99  95        19  99

10            11  10        1  11
10            22  20        2  22
10            33  30        3  33
10            44  40        4  44
10            55  50        5  55
10            66  60        6  66
10            77  70        7  77
10            88  80        8  88
10            99  90        9  99

12            27  24        2  27
12            54  48        4  54
12            81  72        6  81

20            99  80        4  99

25            33  25        1  33
25            66  50        2  66
25            99  75        3  99

28            77  56        2  77

34            51  34        1  51

40            66  40        1  66

45            81  45        1  81

50            99  50        1  99

(blank lines inserted manually between p values)

So p can be 2, 4, 5, 10, 12, 20, 25, 28, 34, 40, 45 or 50

among which

p = 4, 10, 12 and 25 lead to multiple solutions.

 Posted by Charlie on 2012-08-13 12:43:47

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