In an examination, the average marks obtained by John in English, Maths, Hindi and Drawing together are 50. His average marks in Maths, Science, Social Studies and Craft are 70. If the average marks in all seven subjects taken together is 58, what were his marks in Maths?

Introduction / Context:
This problem uses overlapping averages of different subject groups to find John's marks in a particular subject, Maths. By converting each given average into a total and carefully combining these totals, we can solve for the unknown score.

Given Data / Assumptions:
• Subjects: English (E), Maths (M), Hindi (H), Drawing (D), Science (Sc), Social Studies (SS), Craft (C).• Average of E, M, H, D = 50.• Average of M, Sc, SS, C = 70.• Average of all seven subjects = 58.• All averages are computed over John's marks in those subjects.

Concept / Approach:
The plan is to convert each average into a total sum. The total of all seven subjects equals the sum of the first four subjects plus the sum of the last three subjects. Since one of the groups with average 70 includes Maths, we express the last three subjects in terms of M and substitute into the total for all seven. This yields an equation in M which we solve to find the Maths marks.

Step-by-Step Solution:
Step 1: From the first average, E + M + H + D = 4 * 50 = 200.Step 2: From the second average, M + Sc + SS + C = 4 * 70 = 280.Step 3: Let T be the total marks in all seven subjects. From the overall average, T = 7 * 58 = 406.Step 4: T can also be written as (E + M + H + D) + (Sc + SS + C).Step 5: From Step 1, E + M + H + D = 200.Step 6: From Step 2, Sc + SS + C = 280 - M.Step 7: Substitute into T: T = 200 + (280 - M) = 480 - M.Step 8: Using T = 406, we have 480 - M = 406.Step 9: Rearranging, M = 480 - 406 = 74.

Verification / Alternative check:
With M = 74, we have Sc + SS + C = 280 - 74 = 206. The total of all seven subjects is then 200 + 206 = 406. The overall average is 406 / 7 = 58, which matches the given condition. All relationships are satisfied, confirming that John scored 74 in Maths.

Why Other Options Are Wrong:
50, 52, 60: Substituting any of these into the equation T = 480 - M gives totals that do not equal 406. The resulting overall average would not be 58, so these values violate the given conditions.

Common Pitfalls:
Students may incorrectly assume that the Maths marks are the simple average of the two given group averages or may forget to subtract M properly when expressing Sc + SS + C. Carefully keeping track of the overlapping subject (Maths) and using algebra to express totals helps avoid such mistakes.

Final Answer:
John's marks in Maths were 74.