Rama's expenditures and savings are in the ratio 5: 3. if her income increases by 12% and expenditure by 15%, then by how much per cent do her savings increase?

Options

A. 0.12
B. 0.07
C. 0.08
D. 0.13

Answer

To solve the problem step by step, we will follow the given ratios and the percentage increases in income and expenditure to find the percentage increase in savings.

### Step 1: Understand the Ratios
Rama's expenditures and savings are in the ratio of 5:3. This means if we let her expenditure be 5x and her savings be 3x for some value of x.

**Hint:** Remember that the ratio tells us the relative sizes of two quantities. Here, expenditures are larger than savings.

### Step 2: Calculate Total Income
Since savings are what remains after expenditures from income, we can express her income (I) as:
\[ I = \text{Expenditure} + \text{Savings} = 5x + 3x = 8x \]

**Hint:** Total income is the sum of expenditures and savings.

### Step 3: Increase in Income and Expenditure
Rama's income increases by 12%, so the new income (I') is:
\[ I' = I + 0.12I = 1.12I = 1.12 \times 8x = 8.96x \]

Rama's expenditure increases by 15%, so the new expenditure (E') is:
\[ E' = E + 0.15E = 1.15E = 1.15 \times 5x = 5.75x \]

**Hint:** When calculating percentage increases, multiply the original amount by (1 + percentage increase).

### Step 4: Calculate New Savings
Now, we can find the new savings (S'):
\[ S' = I' - E' = 8.96x - 5.75x = 3.21x \]

**Hint:** Savings are calculated by subtracting expenditures from income.

### Step 5: Calculate the Increase in Savings
The original savings were 3x, and the new savings are 3.21x. The increase in savings is:
\[ \text{Increase in Savings} = S' - S = 3.21x - 3x = 0.21x \]

**Hint:** The increase in savings is the difference between new savings and original savings.

### Step 6: Calculate the Percentage Increase in Savings
To find the percentage increase in savings, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Savings}}{\text{Original Savings}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{0.21x}{3x} \right) \times 100 = \left( \frac{0.21}{3} \right) \times 100 = 7\% \]

**Hint:** The percentage increase is found by comparing the increase to the original amount.

### Final Answer
The percentage increase in Rama's savings is **7%**.

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