Question

P sold his bicycle to Q at a profit of 10%. Q sold it to R for #209 at a loss of 5%. How much did the bicycle cost
P?

Answer 1

first sale: 1.1*C
second sale: 209=.95*1.1*C
C=209/(.95*1.1)=200

Answer 2

Bob Pursley worked this the short way. Here is the long way to do it.
P paid C for the bicycle.
He sold it for C + 0.1 to Q
Q lost 5% when s/he sold it and the selling price was 209 so
C+0.1C - (C+_0.1C)*0.05 = $209
1.045C = 209
C = $200

Check it.
C paid $200.
C sold it to Q for 10% profit or $220.
Q solid it at 5% loss or 220 - 0.05 = $11 loss. Then 220-11 = 209 which is the sale price bv Q.