Hemant's monthly expenditure is 72\% of his income. If his income is increased by 13\%, then his expenditure and saving increase by Rs. 2160 and 31\% respectively. What is his new expenditure?

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**Solution:**

1. Let Hemant's original income be $ I $ and original expenditure be $ E $.

2. Given, expenditure is 72\% of income:
   $$ E = 0.72I $$

3. Therefore, original saving:
   $$ S = I - E = I - 0.72I = 0.28I $$

4. Income is increased by 13\%, so new income:
   $$ $I_{new} = I \times 1.13 $$$

5. Expenditure increases by Rs. 2160, so new expenditure:
   $$ E_{new} = E + 2160 = 0.72I + 2160 $$

6. Saving increases by 31\%, so new saving:
   $$ S_{new} = S \times 1.31 = 0.28I \times 1.31 = 0.3668I $$

7. New saving can also be expressed as:
   $$ $S_{new} = I_{new} - E_{new} = 1.13I - (0.72I + 2160) = 1.13I - 0.72I - 2160 = 0.41I - 2160$ $$

8. Equate the two expressions for new saving:
   $$ 0.3668I = 0.41I - 2160 $$

9. Rearranging:
   $$ 0.41I - 0.3668I = 2160 $$
   $$ 0.0432I = 2160 $$
   $$$ I = \frac{2160}{0.0432} = 50000$ $$

10. Calculate new expenditure:
    $$ $E_{new} = 0.72 \times 50000 + 2160 = 36000 + 2160 = 38160$ $$

**Answer:** Rs. 38160

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