Income of Rahim is Rs 12000 per month and that of Ami is Rs 191520 per annum. If the monthly expenditure of each of them is Rs 9960 per month find the ratio of their monthly savings

Answer

To find the ratio of the monthly savings of Rahim and Ami, we will follow these steps:

### Step 1: Determine Rahim's Monthly Savings
- Rahim's monthly income = Rs 12,000
- Rahim's monthly expenditure = Rs 9,960
- Monthly savings of Rahim = Monthly income - Monthly expenditure
\[ \text{Monthly savings of Rahim} = 12000 - 9960 = 2040 \]

### Step 2: Determine Ami's Monthly Income
- Ami's annual income = Rs 191,520
- To find Ami's monthly income, we divide the annual income by 12 (the number of months in a year):
\[ \text{Monthly income of Ami} = \frac{191520}{12} \]
Performing the division:
\[ 191520 \div 12 = 15960 \]

### Step 3: Determine Ami's Monthly Savings
- Ami's monthly income = Rs 15,960
- Ami's monthly expenditure = Rs 9,960
- Monthly savings of Ami = Monthly income - Monthly expenditure
\[ \text{Monthly savings of Ami} = 15960 - 9960 = 6000 \]

### Step 4: Find the Ratio of Monthly Savings
- Now, we need to find the ratio of Rahim's savings to Ami's savings:
\[ \text{Ratio} = \frac{\text{Savings of Rahim}}{\text{Savings of Ami}} = \frac{2040}{6000} \]

### Step 5: Simplify the Ratio
- To simplify the ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). First, we can simplify by dividing by 2:
\[ \frac{2040 \div 2}{6000 \div 2} = \frac{1020}{3000} \]
- We can simplify further by dividing again by 2:
\[ \frac{1020 \div 2}{3000 \div 2} = \frac{510}{1500} \]
- We can simplify once more by dividing by 30:
\[ \frac{510 \div 30}{1500 \div 30} = \frac{17}{50} \]

### Final Answer
The ratio of Rahim's monthly savings to Ami's monthly savings is:
\[ \text{Ratio} = 17 : 50 \]

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