The monthly salary of a person was ₹50,000. He used to spend on three heads- personal and family expenses (E), taxes (T), philanthropy (P), and rest were his savings. E was 50% of the income, T was 20% of E and P was 15% of T. When his salary got raised by 40%, he maintained the percentage level of E, but T became 30% of E and P became 20% of T. By whatpercentage is the new savings more or less than the earlier savings? (correct up to one decimal place)

Options

A. 16.4% more
B. 8.2% more
C. 16.4% less
D. 8.2% less

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Calculate the initial expenses (E), taxes (T), and philanthropy (P) from the original salary.

1. **Given Salary (I)**: ₹50,000
2. **Calculate E (Expenses)**:
- E = 50% of I = 0.5 × 50,000 = ₹25,000
3. **Calculate T (Taxes)**:
- T = 20% of E = 0.2 × 25,000 = ₹5,000
4. **Calculate P (Philanthropy)**:
- P = 15% of T = 0.15 × 5,000 = ₹750

### Step 2: Calculate the initial savings (S).

5. **Calculate Total Expenses**:
- Total Expenses = E + T + P = 25,000 + 5,000 + 750 = ₹30,750
6. **Calculate Initial Savings (S)**:
- S = I - Total Expenses = 50,000 - 30,750 = ₹19,250

### Step 3: Calculate the new salary after the raise.

7. **Calculate New Salary**:
- New Salary = Original Salary + 40% of Original Salary = 50,000 + (0.4 × 50,000) = 50,000 + 20,000 = ₹70,000

### Step 4: Calculate new expenses (E, T, P) based on the new salary.

8. **Calculate New E (Expenses)**:
- New E = 50% of New Salary = 0.5 × 70,000 = ₹35,000
9. **Calculate New T (Taxes)**:
- New T = 30% of New E = 0.3 × 35,000 = ₹10,500
10. **Calculate New P (Philanthropy)**:
- New P = 20% of New T = 0.2 × 10,500 = ₹2,100

### Step 5: Calculate the new savings (S).

11. **Calculate Total New Expenses**:
- Total New Expenses = New E + New T + New P = 35,000 + 10,500 + 2,100 = ₹47,600
12. **Calculate New Savings (S)**:
- New S = New Salary - Total New Expenses = 70,000 - 47,600 = ₹22,400

### Step 6: Calculate the percentage change in savings.

13. **Calculate the Change in Savings**:
- Change in Savings = New Savings - Old Savings = 22,400 - 19,250 = ₹3,150
14. **Calculate the Percentage Change**:
- Percentage Change = (Change in Savings / Old Savings) × 100
- Percentage Change = (3,150 / 19,250) × 100 ≈ 16.4%

### Final Result:
The new savings are approximately **16.4% more** than the earlier savings.

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