A man spends a part of his monthly income and saves the rest. The ratio of his expenditure to his savings is 61 : 6. If his monthly income is Rs. 8,710, what is the amount of his monthly savings?

Introduction / Context:
This is a straightforward ratio and proportion question about income, expenditure and savings. The man spends part of his income and saves the rest. The ratio of expenditure to savings is given along with the total income. We must compute the rupee amount that he saves each month, which is a practical example of budgeting and personal finance.

Given Data / Assumptions:

• Monthly income = Rs. 8,710.• Ratio of expenditure to savings = 61 : 6.• Income = expenditure + savings.• We need to find the amount of monthly savings.

Concept / Approach:
The ratio 61 : 6 means that for every 61 units of money spent, 6 units are saved. The total of these parts is 61 + 6 = 67. Since income is the sum of expenditure and savings, the income corresponds to 67 equal parts. By dividing the total income by 67, we can find the value of one part. Then, multiplying that single part value by 6 gives the savings amount. This is a standard application of ratios to divide a total into proportional segments.

Step-by-Step Solution:
Step 1: Let expenditure be 61x and savings be 6x.Step 2: Then income = expenditure + savings = 61x + 6x = 67x.Step 3: We are told that income is Rs. 8,710, so 67x = 8,710.Step 4: Solve for x: x = 8,710 / 67.Step 5: Perform the division: 8,710 / 67 = 130.Step 6: Now compute savings = 6x = 6 * 130 = 780 rupees.Step 7: Therefore, the man saves Rs. 780 each month.

Verification / Alternative check:
We can verify by also computing the expenditure. Expenditure = 61x = 61 * 130 = 7,930. Now check the total: expenditure + savings = 7,930 + 780 = 8,710, which matches the monthly income. Also, the ratio expenditure : savings = 7,930 : 780. Dividing both by 130 gives 61 : 6, which matches the ratio given in the question. This confirms that the savings amount has been computed correctly.

Why Other Options Are Wrong:
• Rs. 870: If savings were 870, the implied ratio of expenditure to savings and the total income would not satisfy the given condition.• Rs. 690: This is too low and would yield the wrong ratio when combined with the corresponding expenditure.• Rs. 980: This is too high and would not keep expenditure and savings in the correct ratio while summing to Rs. 8,710.

Common Pitfalls:
Some students mistakenly interpret the ratio 61 : 6 as expenditure : income instead of expenditure : savings. Others forget to add the ratio parts when equating to total income and incorrectly use either 61 or 6 alone for division. Arithmetic mistakes in dividing 8,710 by 67 can also lead to incorrect answers. Carefully identifying what each part of the ratio represents and keeping track of income as the sum of expenditure and savings is essential.

Final Answer:
The man saves Rs. 780 every month.