A shopkeeper sells two bicycles, each purchased at a cost price of $p, to John and Mike at a profit of 15% and at a loss of 15%, respectively. John sells his bicycle to Robert at a profit of 25%, while Mike sells his bicycle to Peter at a loss of 25%. If Robert pays $x for the bicycle and Peter pays $y for the bicycle, then the ratio of the absolute difference between the amounts paid by Robert and Peter for the bicycle to the actual cost of the bicycles is:

Let the initial cost price of each bicycle be 100p, making Robert's final cost 100p x 1.15 x 1.25 = 143.75p and Peter's final cost 100p x 0.85 x 0.75 = 63.75p. The absolute difference between the amounts they paid is 143.75p - 63.75p = 80p. Since the actual cost of the two bicycles bought by the shopkeeper was 200p (100p each), the ratio of the difference to the actual cost is 80p : 200p, which simplifies to 2 : 5.

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