The monthly earnings of Alex are 22.5% greater than those of Brian, whereas Alex's monthly expenditures exceed Brian's expenditures by Rs.15000. If Alex manages to save Rs.3000 more than Brian each month, calculate Brian's monthly earnings.

The correct option is Rs.80000.

Step-by-Step Explanation:

Let Brian's monthly earnings be E_B and Brian's monthly expenditures be X_B.

Alex's monthly earnings are 22.5% greater than Brian's monthly earnings:

$E_A=E_B+0.225E_B=1.225E_B$

Alex's monthly expenditures exceed Brian's expenditures by Rs.15000:

$X_A=X_B+15000$

Savings are given by the formula: Savings = Earnings - Expenditures.

Brian's monthly savings:

$S_B=E_B-X_B$

Alex's monthly savings:

$S_A=E_A-X_A=1.225E_B-(X_B+15000)$

It is given that Alex manages to save Rs.3000 more than Brian each month:

$S_A=S_B+3000$

Substitute the expressions for savings into the equation:

$1.225E_B-X_B-15000=E_B-X_B+3000$

Subtract $(E_B-X_B)$ from both sides:

$0.225E_B-15000=3000$

Add 15000 to both sides:

$0.225E_B=18000$

Solve for Brian's monthly earnings E_B:

$E_B=\frac{18000}{0.225}=80000$

Therefore, Brian's monthly earnings are Rs.80000.