The salaries of two friends A and B are in the ratio $3:4$, and their expenditures are in the ratio $1:2$. Both A and B save Rs $6000$ each. If B spends an additional $20\%$ of his salary, what will be B's new savings (in Rs)?

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**Solution:**

1. Let the salaries of A and B be $3x$ and $4x$ respectively.

2. Let the expenditures of A and B be $y$ and $2y$ respectively (since expenditure ratio is $1:2$).

3. Given savings of A and B are Rs $6000$ each.

For A: Savings = Salary - Expenditure

$$6000 = 3x - y \implies y = 3x - 6000$$

For B: Savings = Salary - Expenditure

$$6000 = 4x - 2y$$

4. Substitute $y$ from A's equation into B's equation:

$$6000 = 4x - 2(3x - 6000) = 4x - 6x + 12000 = -2x + 12000$$

5. Rearranging:

$$-2x = 6000 - 12000 = -6000 \implies x = 3000$$

6. Now, calculate $y$:

$$y = 3(3000) - 6000 = 9000 - 6000 = 3000$$

7. B's salary = $4x = 4 	imes 3000 = 12000$

B's expenditure = $2y = 2 	imes 3000 = 6000$

B's initial savings = $12000 - 6000 = 6000$ (which matches given data)

8. Now, B spends an additional $20\%$ of his salary:

Additional expenditure = $20\%$ of $12000 = 0.20 	imes 12000 = 2400$

9. New expenditure of B = $6000 + 2400 = 8400$

10. New savings of B = Salary - New expenditure

$$= 12000 - 8400 = 3600$$

**Answer:** Rs $3600$

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