A man spends a part of his monthly income and saves the rest. The ratio of his expenditure to the saving is 61: 6. If his monthly income is t 8710, the amount of his monthly savings is/एक व्यक्ति अपनी मासिक आय का कुछ भाग खर्च करता है और बाकी की बचत करता है। उसके व्यय और बचत का अनुपात `61:6` है। यदि उसकी मासिक आय ₹ 8710 हो, तो उसकी मासिक बचत की राशि कितनी है ?

Options

A. 870
B. 690
C. 980
D. 780

Explanation

To solve the problem step by step, we will follow the information provided in the question and the video transcript.

### Step 1: Understand the Ratios
The ratio of expenditure to savings is given as 61:6. This means that for every 67 parts (61 parts expenditure + 6 parts savings), 61 parts are spent and 6 parts are saved.

### Step 2: Set Up the Equation
Let the common multiple be \( x \). Therefore:
- Expenditure = \( 61x \)
- Savings = \( 6x \)

### Step 3: Total Income Equation
According to the problem, the total income is the sum of expenditure and savings:
\[ \text{Expenditure} + \text{Savings} = \text{Income} \]
This can be written as:
\[ 61x + 6x = 8710 \]
Combining the terms gives:
\[ 67x = 8710 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides by 67:
\[ x = \frac{8710}{67} \]
Calculating this gives:
\[ x = 130 \]

### Step 5: Calculate Monthly Savings
Now that we have \( x \), we can find the amount of savings:
\[ \text{Savings} = 6x = 6 \times 130 = 780 \]

### Conclusion
The amount of his monthly savings is **₹ 780**.

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