The monthly income of Rajesh is 22.5\% more than that of Rakesh, while Rajesh's expenditure is Rs.15000 more than Rakesh's expenditure. If Rajesh's savings exceed Rakesh's savings by Rs.3000, what is the monthly income of Rakesh?

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**Solution:**

1. Let the monthly income of Rakesh be $ x $.

2. Rajesh's income is 22.5\% more than Rakesh's, so Rajesh's income = $ x + 0.225x = 1.225x $.

3. Let the expenditure of Rakesh be $ y $. Then, Rajesh's expenditure = $ y + 15000 $.

4. Savings are defined as income minus expenditure.
   - Savings of Rakesh = $ x - y $
   - Savings of Rajesh = $ 1.225x - (y + 15000) = 1.225x - y - 15000 $

5. Given that Rajesh's savings are Rs.3000 more than Rakesh's savings:
   $$
  $ (1.225x - y - 15000) - (x - y) = 3000$
   $$

6. Simplify the equation:
   $$
   1.225x - y - 15000 - x + y = 3000
   $$
   $$
   1.225x - x - 15000 = 3000
   $$
   $$
   0.225x = 18000
   $$

7. Solve for $ x $:
   $$
  $ x = \frac{18000}{0.225} = 80000$
   $$

**Answer:** Rs.80000

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