Monthly income of Ramesh is Rs. 5000 and he spends it in ratio 2 : 5 on clothes and food. If price of clothes is increased by `10%` and price of food is increased by `20%` , then by how much percent his income should be increased so that the ratio of his expenditure remains the same.

Answer

To solve the problem step by step, we will follow the given information and calculations systematically.

### Step 1: Determine Ramesh's Expenditure on Clothes and Food
Ramesh's monthly income is Rs. 5000, and he spends it in the ratio of 2:5 on clothes and food.

**Calculation:**
- Total parts in the ratio = 2 + 5 = 7 parts
- Expenditure on clothes = (2/7) * 5000 = Rs. 1428.57 (approximately)
- Expenditure on food = (5/7) * 5000 = Rs. 3571.43 (approximately)

### Step 2: Calculate the New Prices After Increases
The price of clothes is increased by 10%, and the price of food is increased by 20%.

**Calculation:**
- New expenditure on clothes = 1428.57 + (10/100 * 1428.57) = 1428.57 + 142.86 = Rs. 1571.43 (approximately)
- New expenditure on food = 3571.43 + (20/100 * 3571.43) = 3571.43 + 714.29 = Rs. 4285.72 (approximately)

### Step 3: Calculate the Total New Expenditure
Now, we need to find the total new expenditure after the price increases.

**Calculation:**
- Total new expenditure = New expenditure on clothes + New expenditure on food
- Total new expenditure = 1571.43 + 4285.72 = Rs. 5857.15 (approximately)

### Step 4: Determine the Required Income to Maintain the Same Ratio
To maintain the same ratio of expenditure (2:5), we need to find out what Ramesh's new income should be.

**Calculation:**
Let the new income be \( x \).
- The new expenditure on clothes should be \( \frac{2}{7}x \)
- The new expenditure on food should be \( \frac{5}{7}x \)

Setting the total new expenditure equal to the sum of the new expenditures:
\[ \frac{2}{7}x + \frac{5}{7}x = 5857.15 \]
\[ \frac{7}{7}x = 5857.15 \implies x = 5857.15 \]

### Step 5: Calculate the Increase in Income
Now we need to find out how much Ramesh's income needs to increase from Rs. 5000 to Rs. 5857.15.

**Calculation:**
- Increase in income = New income - Old income
- Increase = 5857.15 - 5000 = Rs. 857.15 (approximately)

### Step 6: Calculate the Percentage Increase in Income
Finally, we calculate the percentage increase in Ramesh's income.

**Calculation:**
\[ \text{Percentage Increase} = \left(\frac{\text{Increase}}{\text{Old Income}}\right) \times 100 \]
\[ \text{Percentage Increase} = \left(\frac{857.15}{5000}\right) \times 100 \approx 17.14\% \]

### Final Answer
Ramesh's income should be increased by approximately **17.14%** to maintain the same ratio of expenditure on clothes and food.

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