The expenditure and income of Manoj are in the ratio of `5: 8`. After some time income of Manoj is increased by `20%` but at the same time his saving is also increased by `3 (1)/(3)%`. Find increased or decreased percent in his expenditure.

Options

A. `24%`
B. `30%`
C. `20%`
D. `15%`

Answer

To solve the problem step by step, we will follow the information given about Manoj's income, expenditure, and savings.

### Step 1: Define the initial income and expenditure
Given the ratio of expenditure to income is 5:8, we can assume:
- Expenditure = 5x
- Income = 8x

### Step 2: Calculate the initial savings
Savings can be calculated as:
\[ \text{Savings} = \text{Income} - \text{Expenditure} \]
Substituting the values:
\[ \text{Savings} = 8x - 5x = 3x \]

### Step 3: Calculate the new income after a 20% increase
The income is increased by 20%. Therefore, the new income will be:
\[ \text{New Income} = \text{Old Income} + 20\% \text{ of Old Income} \]
\[ \text{New Income} = 8x + 0.2 \times 8x = 8x \times 1.2 = 9.6x \]

### Step 4: Calculate the new savings after a 3 (1/3)% increase
The increase in savings is given as \(3 \frac{1}{3}\%\), which can be converted to a fraction:
\[ 3 \frac{1}{3}\% = \frac{10}{3}\% \]
To find the new savings:
\[ \text{New Savings} = \text{Old Savings} + \frac{10}{3}\% \text{ of Old Savings} \]
\[ \text{New Savings} = 3x + \left(\frac{10}{3} \times \frac{3x}{100}\right) \]
\[ \text{New Savings} = 3x + \frac{10x}{100} = 3x + 0.1x = 3.1x \]

### Step 5: Calculate the new expenditure
Using the new income and new savings, we can find the new expenditure:
\[ \text{New Expenditure} = \text{New Income} - \text{New Savings} \]
\[ \text{New Expenditure} = 9.6x - 3.1x = 6.5x \]

### Step 6: Calculate the change in expenditure
To find the change in expenditure, we subtract the old expenditure from the new expenditure:
\[ \text{Change in Expenditure} = \text{New Expenditure} - \text{Old Expenditure} \]
\[ \text{Change in Expenditure} = 6.5x - 5x = 1.5x \]

### Step 7: Calculate the percentage change in expenditure
Now, we calculate the percentage change in expenditure:
\[ \text{Percentage Change} = \left(\frac{\text{Change in Expenditure}}{\text{Old Expenditure}}\right) \times 100 \]
\[ \text{Percentage Change} = \left(\frac{1.5x}{5x}\right) \times 100 = \left(\frac{1.5}{5}\right) \times 100 = 30\% \]

### Final Answer
The expenditure has increased by **30%**.

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