A grocer records monthly sales of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for five consecutive months. What sales amount must he achieve in the sixth month so that his average monthly sales for all six months is Rs. 6500?

Introduction / Context:
This aptitude question tests the concept of arithmetic mean applied to monthly sales. A grocer has sales figures for five months and wants to know what sales are required in the sixth month to reach a target average of Rs. 6500. Such questions are very common in banking, SSC and placement exams because they check the ability to reverse engineer an unknown value from a required average.

Given Data / Assumptions:
- Sales for the first five months: Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562.
- Total number of months to be considered: 6.
- Required average monthly sale for all six months: Rs. 6500.
- Let the sales in the sixth month be x rupees.

Concept / Approach:
The arithmetic mean or average of a set of values is defined as total sum of the values divided by the number of values. When the desired average and some of the values are known, we can find the missing value by first computing the required total sum and then subtracting the known sum. Here we will compute the total sales required for six months and then deduce the sixth month sales from it.

Step-by-Step Solution:
Step 1: Required total sales for six months = required average * number of months = 6500 * 6 = Rs. 39000.Step 2: Compute the sum of the known five months: 6435 + 6927 + 6855 + 7230 + 6562 = Rs. 34009.Step 3: Let the required sales in the sixth month be x. Then total sales for six months = 34009 + x.Step 4: Equate this to the required total sales: 34009 + x = 39000.Step 5: Solve for x: x = 39000 - 34009 = Rs. 4991.

Verification / Alternative Check:
If the grocer sells Rs. 4991 in the sixth month, the total of all six months becomes 34009 + 4991 = Rs. 39000. Dividing by 6 gives 39000 / 6 = Rs. 6500, which exactly matches the required average. This confirms that the computed value is correct and consistent with the definition of average.

Why Other Options Are Wrong:
Rs. 5467, Rs. 5987 and Rs. 6453 all produce a total that is greater than or less than Rs. 39000, giving an average different from Rs. 6500. For example, if the sixth month sales were Rs. 6453, the total would be 34009 + 6453 = 40462 and the average would be 40462 / 6 which is greater than Rs. 6500. Therefore these values do not satisfy the required average condition.

Common Pitfalls:
A common mistake is to average the given five months first and then try to adjust by intuition instead of using the formula. Another frequent error is to divide by 5 instead of 6 when calculating the required total or to forget that the target average applies to all six months together. Some learners also accidentally add 6500 instead of multiplying 6500 by 6. Careful use of the average formula avoids these issues.

Final Answer:
The grocer must have sales of Rs. 4991 in the sixth month to obtain an average monthly sale of Rs. 6500.