Explanation:

- The sum of the cost prices of two bikes is Rs 50,000. We can express this as:

$C{P}_1+C{P}_2=50,000$

- The first bike is sold at a 20% profit. Selling Price (SP) of the first bike is:

$S{P}_1=C{P}_1\times 1.2$

- The second bike is sold at a 20% loss. Selling Price (SP) of the second bike is:

$S{P}_2=C{P}_2\times 0.8$

- Both bikes are sold at the same selling price, so:

$C{P}_1\times 1.2=C{P}_2\times 0.8$

- Solving these equations simultaneously:

- From $C{P}_1+C{P}_2=50,000$ and $1.2C{P}_1=0.8C{P}_2$,

we can write $C{P}_1=2C{P}_2/3$.

- Substituting in the first equation:

$\frac{2}{3}C{P}_2+C{P}_2=50,000$

$\frac{5}{3}C{P}_2=50,000$

$C{P}_2=30,000$

- Therefore, the cost price of the second bike is Rs 30,000.

- Option: 3 - 30,000 is the correct answer.