The annual earning of Mr. Sikkawala is Rs, 4 lakhs per annum for the first yeat of his job and his expenditure was 50%. Later on for the next 3 years his average income increases by Rs. 40,000 per annum and the saving was 40%, 30% and 20% of the income. What is the percentage of his total savings over the total expenditure if there is no any interest is applied on the savings for these four years :

Options

A. a. `49(37)/(87)%`
B. b. `41(73)/(83)%`
C. c. 0.53
D. d. none of these

Answer

To solve the problem step by step, we will calculate Mr. Sikkawala's income, expenditure, and savings for each of the four years, and then find the total savings and total expenditure to determine the percentage of savings over expenditure.

### Step 1: Calculate the income, expenditure, and savings for the first year.
- **Income for Year 1**: Rs. 4,00,000
- **Expenditure for Year 1**: 50% of Income = 50% of Rs. 4,00,000 = Rs. 2,00,000
- **Savings for Year 1**: Income - Expenditure = Rs. 4,00,000 - Rs. 2,00,000 = Rs. 2,00,000

### Step 2: Calculate the income, expenditure, and savings for the second year.
- **Income for Year 2**: Rs. 4,00,000 + Rs. 40,000 = Rs. 4,40,000
- **Savings for Year 2**: 40% of Income = 40% of Rs. 4,40,000 = Rs. 1,76,000
- **Expenditure for Year 2**: Income - Savings = Rs. 4,40,000 - Rs. 1,76,000 = Rs. 2,64,000

### Step 3: Calculate the income, expenditure, and savings for the third year.
- **Income for Year 3**: Rs. 4,40,000 + Rs. 40,000 = Rs. 4,80,000
- **Savings for Year 3**: 30% of Income = 30% of Rs. 4,80,000 = Rs. 1,44,000
- **Expenditure for Year 3**: Income - Savings = Rs. 4,80,000 - Rs. 1,44,000 = Rs. 3,36,000

### Step 4: Calculate the income, expenditure, and savings for the fourth year.
- **Income for Year 4**: Rs. 4,80,000 + Rs. 40,000 = Rs. 5,20,000
- **Savings for Year 4**: 20% of Income = 20% of Rs. 5,20,000 = Rs. 1,04,000
- **Expenditure for Year 4**: Income - Savings = Rs. 5,20,000 - Rs. 1,04,000 = Rs. 4,16,000

### Step 5: Calculate total savings and total expenditure over the four years.
- **Total Savings**:
- Year 1: Rs. 2,00,000
- Year 2: Rs. 1,76,000
- Year 3: Rs. 1,44,000
- Year 4: Rs. 1,04,000
- Total Savings = Rs. 2,00,000 + Rs. 1,76,000 + Rs. 1,44,000 + Rs. 1,04,000 = Rs. 6,24,000

- **Total Expenditure**:
- Year 1: Rs. 2,00,000
- Year 2: Rs. 2,64,000
- Year 3: Rs. 3,36,000
- Year 4: Rs. 4,16,000
- Total Expenditure = Rs. 2,00,000 + Rs. 2,64,000 + Rs. 3,36,000 + Rs. 4,16,000 = Rs. 12,16,000

### Step 6: Calculate the percentage of total savings over total expenditure.
- **Percentage of Savings over Expenditure** = (Total Savings / Total Expenditure) × 100
- **Calculation**:
- (Rs. 6,24,000 / Rs. 12,16,000) × 100 = 51.25%

### Final Result:
The percentage of Mr. Sikkawala's total savings over his total expenditure is approximately **51.25%**.