Let the mass of the bicycle we started with and which has to be determined be W kg. Changing the alloy of the frame can reduce the mass by 13%, the mass is now `(1-0.13)*W` . Changing the tires reduces mass by a further 2 kg. The present mass is `(1-0.13)*W - 2` . If a lighter paint is used, the present mass can be reduced by 3%, This gives the final mass in terms of W as `((1-0.13)*W - 2)*(1 - 0.03)` . As this is equal to 15 kg,

`((1-0.13)*W - 2)*(1 - 0.03) = 15`

=> `(1-0.13)*W - 2 = 15/0.97`

=> `(1-0.13)*W = 15/0.97 + 2`

=> `W = (15/0.97 + 2)/(0.87)`

=> `W ~~ 20.07` kg

**The initial mass of the bicycle prior to making the changes is 20.07 kg**

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