A student's average marks in 7 subjects is 85. His average in 6 subjects, excluding English, is 83. What marks did he score in English?

Introduction / Context:
This is another average and total marks problem where we must isolate one subject's marks given two different averages. It reinforces the idea that averages can always be converted back into totals, which then allows us to find the missing value by simple subtraction.

Given Data / Assumptions:

• The student has 7 subjects in total.

• Average marks in all 7 subjects = 85.

• Average marks in 6 subjects, excluding English, = 83.

• All marks are on the same scale and additive.

• We need the marks obtained in English.

Concept / Approach:
We first compute the grand total of marks for all 7 subjects from the given overall average. Next, we compute the total marks for the 6 subjects other than English using their average. The difference between the grand total and the 6 subject total must be the marks in English. This exploits the relationship total = average * number of items and the fact that the overall total is the sum of all individual subject scores.

Step-by-Step Solution:
Total marks in 7 subjects = 7 * 85 = 595. Total marks in the 6 subjects excluding English = 6 * 83 = 498. Marks in English = total marks for 7 subjects − total marks for the other 6 subjects. Marks in English = 595 − 498 = 97.

Verification / Alternative check:
We can reconstruct the averages as a check. Suppose English marks are 97, and the sum of the other 6 subjects is 498. Then total = 498 + 97 = 595. The overall average = 595 / 7 = 85, which matches the original data. For the 6 subjects excluding English, the average is 498 / 6 = 83, also matching the given information. This double confirmation shows that 97 is correct.

Why Other Options Are Wrong:
If English were 98, then the total marks would be 498 + 98 = 596 and the average over 7 subjects would be 596 / 7, which is not 85. Similarly, English marks of 92 or 93 would lead to totals and averages that do not satisfy both the 7 subject and 6 subject averages. Only 97 maintains both conditions at the same time.

Common Pitfalls:
Some students mistakenly divide rather than subtract or try to re average the 6 subjects in a complicated way. Others miscalculate the totals due to small arithmetic errors. It is helpful to always write down the two totals clearly and then subtract them, followed by a quick recomputation of the averages to verify the result.

Final Answer:
The student scored 97 marks in English.