Between two consecutive years, my income is in the ratio 2 : 5 and expenses are in the ratio 4: 7. If my income in the second year is Rs. 75,000 and my expenses in the first year are Rs. 20,000, then my total savings in the two years together are:

Options

A. Rs. 55,000
B. Rs. 60,000
C. Rs. 50,000
D. Rs. 40,000

Answer

To solve the problem step by step, we will break down the information given and use it to calculate the total savings for the two years.

### Step 1: Understand the Ratios
We know that:
- The income ratio between the first year and the second year is 2:5.
- The expenses ratio between the first year and the second year is 4:7.

Let’s denote:
- Income in the first year = 2X
- Income in the second year = 5X
- Expenses in the first year = 4Y
- Expenses in the second year = 7Y

### Step 2: Use Given Information
From the problem:
- Income in the second year = Rs. 75,000
- Expenses in the first year = Rs. 20,000

### Step 3: Set Up Equations
From the income in the second year:
\[ 5X = 75,000 \]
To find X:
\[ X = \frac{75,000}{5} = 15,000 \]

From the expenses in the first year:
\[ 4Y = 20,000 \]
To find Y:
\[ Y = \frac{20,000}{4} = 5,000 \]

### Step 4: Calculate Income and Expenses for Both Years
Now we can calculate the income and expenses for both years:
- Income in the first year:
\[ 2X = 2 \times 15,000 = 30,000 \]

- Expenses in the second year:
\[ 7Y = 7 \times 5,000 = 35,000 \]

### Step 5: Calculate Savings for Each Year
Now, we can calculate the savings for each year:
- Savings in the first year:
\[ \text{Savings}_1 = \text{Income}_1 - \text{Expenses}_1 = 30,000 - 20,000 = 10,000 \]

- Savings in the second year:
\[ \text{Savings}_2 = \text{Income}_2 - \text{Expenses}_2 = 75,000 - 35,000 = 40,000 \]

### Step 6: Calculate Total Savings
Now, we can find the total savings over the two years:
\[ \text{Total Savings} = \text{Savings}_1 + \text{Savings}_2 = 10,000 + 40,000 = 50,000 \]

### Final Answer
The total savings in the two years together are Rs. 50,000.

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