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 Feet-Inch Transpose (Posted on 2013-12-06)
(A) Ben called ahead by telephone and ordered a length of rope which is in integer feet and inches (that is, lengths like 3 feet and 5 inches NOT lengths like 3 feet and 5.5 inches. Also, lengths like 3 feet and 34 inches are untenable.)

When he picked it up, he found that the clerk had wrongly written the order by interchanging the feet and inches. As a result the rope was only 30% of the length he ordered.

What length did he originally order and what length did he get?

(B) If Ben had got p% of the length he ordered, then for what integer values of p from 1 to 100 inclusive are each of the length of the rope he ordered and the length of the rope he received in integer feet and inches?

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 2 of 7 |

10   for F=0 to 11
20   for I=0 to 11
30    Ord=12*F+I:Got=12*I+F
35    if Ord>0 then
40    :Pct=100*(Got//Ord)
50    :if Pct=int(Pct) and Pct<100 then print F;I,Pct
60   next
70   next

lists the ways of getting all percentages below 100.

`orderedft inch  pct 2  1    56 4  2    56 6  3    56 8  4    56 9  2    30 10  5   56 `

Only 30% and 56% are possible, other than the 100% that doesn't involve transposition.

In the particular case of (A), he asked for 9'2" and got 2'9", or only 30% of his order.

`orderedft inch  pct0  1    12000  2    12000  3    12000  4    12000  5    12000  6    12000  7    12000  8    12000  9    12000  10   12000  11   12001  8    4851  10   5503  8    2254  7    160`

 Posted by Charlie on 2013-12-06 17:05:59

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