Amitabh's average monthly expenditure from January to June is Rs 4200. He spends Rs 1200 in January and Rs 1500 in July. What is his average monthly expenditure from February to July (a total of six months)?

Introduction / Context:
This problem is about average monthly expenditure over different time periods. We are given Amitabh's average spending from January to June, and specific amounts for January and July. We must then compute his average expenditure from February to July. The key idea is to convert averages into total sums and then recompute averages for the required months.

Given Data / Assumptions:

• Average expenditure from January to June (6 months) = Rs 4200 per month.
• Expenditure in January = Rs 1200.
• Expenditure in July = Rs 1500.
• We need the average expenditure for the months February, March, April, May, June and July (6 months in total).

Concept / Approach:
Average is defined as: average = total / number of months. We first find the total expenditure for January to June by multiplying the average by 6. Then we subtract January's actual expenditure to get the combined expenditure for February to June. After that, we add July's expenditure to get the total for February to July and divide by 6 to compute the new average.

Step-by-Step Solution:
Step 1: Total expenditure from January to June. Total(Jan–Jun) = 6 * 4200 = Rs 25200. Step 2: Expenditure for February to June combined. Total(Feb–Jun) = Total(Jan–Jun) - Expenditure(Jan). Total(Feb–Jun) = 25200 - 1200 = Rs 24000. Step 3: Add July to cover February to July. Total(Feb–Jul) = 24000 + 1500 = Rs 25500. Step 4: Number of months from February to July = 6. Average(Feb–Jul) = Total(Feb–Jul) / 6 = 25500 / 6. Compute 25500 / 6: 6 * 4250 = 25500. Therefore, average = Rs 4250.
Verification / Alternative check:
We can double-check the arithmetic: 6 * 4200 = 25200 is correct; subtracting 1200 gives 24000; adding 1500 gives 25500; and 25500 / 6 indeed equals 4250.
Why Other Options Are Wrong:
Rs 4520 and Rs 4300 are higher than the correctly computed average, implying unrealistically high totals for February to July. Rs 4060 is lower and would not match the known totals for the months. Hence only Rs 4250 is consistent with all the data.
Common Pitfalls:
One common mistake is to incorrectly treat Rs 4200 as also being the individual monthly expenditure for each month, instead of using it only to find the total. Another error is forgetting to include July when computing the new total or miscounting the number of months in the new average.
Final Answer:
The average monthly expenditure from February to July is Rs 4250.