A grocer has sales of Rs 6435, Rs 6927, Rs 6855, Rs 7230 and Rs 6562 in five consecutive months. What should be his sales (in rupees) in the sixth month so that his average monthly sale over the six months becomes Rs 6500?

Introduction / Context:
This is an average (mean) based aptitude question involving monthly sales figures. You are given the sales for five consecutive months and asked to find the sixth month's sales so that the overall average becomes a specified amount. Such questions are very common in competitive exams to test understanding of the mean formula and simple algebraic manipulation.

Given Data / Assumptions:

• Sales for month 1 = Rs 6435.
• Sales for month 2 = Rs 6927.
• Sales for month 3 = Rs 6855.
• Sales for month 4 = Rs 7230.
• Sales for month 5 = Rs 6562.
• Desired average sale over 6 months = Rs 6500.
• Let the sale in month 6 be S rupees.

Concept / Approach:
Average (mean) is given by: average = (sum of all values) / (number of values). We first calculate the total sales of the first five months. Then we determine what the total sales must be over six months to get an average of Rs 6500. The difference between this required total and the already known five-month total gives us the required sale in the sixth month.

Step-by-Step Solution:
Step 1: Compute sum of sales for first 5 months. Sum = 6435 + 6927 + 6855 + 7230 + 6562. 6435 + 6927 = 13362. 13362 + 6855 = 20217. 20217 + 7230 = 27447. 27447 + 6562 = 34009. So total for 5 months = Rs 34009. Step 2: Required total for 6 months with average Rs 6500. Required total = 6500 * 6 = 39000. Step 3: Let sale in 6th month be S, then: 34009 + S = 39000. Step 4: Solve for S: S = 39000 - 34009 = 4991.
Verification / Alternative check:
Check the new average: New total = 34009 + 4991 = 39000. Average = 39000 / 6 = 6500, which matches the requirement.
Why Other Options Are Wrong:
Any value other than 4991 will make the total different from 39000, and the average will not be exactly Rs 6500. For example, if S = 5467, total = 39476 and average = 39476 / 6 ≈ 6579.33, which is higher than 6500.
Common Pitfalls:
Students sometimes take the average of the first five months and then adjust, instead of working directly with totals. Another mistake is to divide the difference in totals by 5 instead of 6, confusing the number of months.
Final Answer:
The grocer must have sales of Rs 4991 in the sixth month to achieve an average of Rs 6500 over six months.