Rohit earns ₹15300 and saves ₹ 1224 per month. Find the ratio of
a. his income and savings:
b. his income and expenditure,
c. his expenditure and savings.

Answer

To solve the problem step by step, we will find the ratios of Rohit's income, savings, and expenditure.

### Given:
- Rohit's Income = ₹15,300
- Rohit's Savings = ₹1,224

### Step 1: Calculate Rohit's Expenditure
Rohit's expenditure can be calculated by subtracting his savings from his income.

\[ \text{Expenditure} = \text{Income} - \text{Savings} \]

\[ \text{Expenditure} = ₹15,300 - ₹1,224 = ₹14,076 \]

### Step 2: Find the Ratio of Income and Savings
To find the ratio of Rohit's income to his savings, we write it as:

\[ \text{Ratio of Income to Savings} = \frac{\text{Income}}{\text{Savings}} = \frac{15300}{1224} \]

Now, we simplify this fraction:

1. Divide both the numerator and the denominator by their greatest common divisor (GCD).
2. The GCD of 15300 and 1224 is 612.

\[ \frac{15300 \div 612}{1224 \div 612} = \frac{25}{2} \]

Thus, the ratio of Rohit's income to his savings is:

\[ \text{Income : Savings} = 25 : 2 \]

### Step 3: Find the Ratio of Income and Expenditure
Next, we find the ratio of Rohit's income to his expenditure:

\[ \text{Ratio of Income to Expenditure} = \frac{\text{Income}}{\text{Expenditure}} = \frac{15300}{14076} \]

Again, we simplify this fraction:

1. The GCD of 15300 and 14076 is also 612.

\[ \frac{15300 \div 612}{14076 \div 612} = \frac{25}{23} \]

Thus, the ratio of Rohit's income to his expenditure is:

\[ \text{Income : Expenditure} = 25 : 23 \]

### Step 4: Find the Ratio of Expenditure and Savings
Finally, we find the ratio of Rohit's expenditure to his savings:

\[ \text{Ratio of Expenditure to Savings} = \frac{\text{Expenditure}}{\text{Savings}} = \frac{14076}{1224} \]

We simplify this fraction:

1. The GCD of 14076 and 1224 is again 612.

\[ \frac{14076 \div 612}{1224 \div 612} = \frac{23}{2} \]

Thus, the ratio of Rohit's expenditure to his savings is:

\[ \text{Expenditure : Savings} = 23 : 2 \]

### Summary of Ratios:
- a. Income : Savings = 25 : 2
- b. Income : Expenditure = 25 : 23
- c. Expenditure : Savings = 23 : 2