The ratio of expenditure and savings is 3:2. If the income increases by 15% and the savings increases by 6%, then by how much per cent should his expenditure increases?

Options

A. 25
B. 21
C. 12
D. 24

Answer

To solve the problem step by step, we will follow the given information and calculate the required percentage increase in expenditure.

### Step 1: Understand the given ratio of expenditure and savings
The ratio of expenditure to savings is given as 3:2. This means for every 3 parts of expenditure, there are 2 parts of savings.

### Step 2: Assign values to expenditure and savings
Let us assume:
- Expenditure (E) = 3x
- Savings (S) = 2x

### Step 3: Calculate total income
Total Income (I) can be calculated as:
\[ I = E + S = 3x + 2x = 5x \]

### Step 4: Calculate the increase in income
The income increases by 15%. Therefore, the new income (I') is:
\[ I' = I + 0.15I = 1.15I = 1.15 \times 5x = 5.75x \]

### Step 5: Calculate the increase in savings
The savings increase by 6%. Therefore, the new savings (S') is:
\[ S' = S + 0.06S = 1.06S = 1.06 \times 2x = 2.12x \]

### Step 6: Calculate the new expenditure
Since the new income is the sum of new savings and new expenditure, we can express the new expenditure (E') as:
\[ I' = E' + S' \]
Substituting the values we have:
\[ 5.75x = E' + 2.12x \]
Now, solving for E':
\[ E' = 5.75x - 2.12x = 3.63x \]

### Step 7: Calculate the increase in expenditure
The original expenditure was \( E = 3x \). The new expenditure is \( E' = 3.63x \). Therefore, the increase in expenditure is:
\[ \text{Increase in Expenditure} = E' - E = 3.63x - 3x = 0.63x \]

### Step 8: Calculate the percentage increase in expenditure
The percentage increase in expenditure can be calculated as:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Expenditure}}{\text{Original Expenditure}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{0.63x}{3x} \right) \times 100 = \left( \frac{0.63}{3} \right) \times 100 = 21\% \]

### Final Answer
The expenditure should increase by **21%**.

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