Two-subject marks with linear relations One-third of Rahul's Mathematics marks exceeds one-half of his Hindi marks by 30. If together he scored 480 in these two subjects, how many marks did he get in Hindi?

Introduction / Context:
This problem converts wording into simultaneous linear equations. It assesses your skill in forming equations from verbal conditions and solving them cleanly by substitution or elimination.

Given Data / Assumptions:

• M = marks in Mathematics; H = marks in Hindi.
• (1/3)M exceeds (1/2)H by 30 ⇒ (1/3)M − (1/2)H = 30.
• Total marks: M + H = 480.
• We assume marks are nonnegative and the algebra is exact.

Concept / Approach:
Translate the comparison into an equation and combine it with the total. Use elimination by clearing denominators to avoid fractional coefficients, then solve systematically for H first (or M first) as convenient.

Step-by-Step Solution:
(1/3)M − (1/2)H = 30.Multiply by 6 to clear fractions: 2M − 3H = 180.Also given: M + H = 480.From 2M − 3H = 180 ⇒ 2M = 180 + 3H ⇒ M = 90 + 1.5H.Substitute in M + H = 480: (90 + 1.5H) + H = 480 ⇒ 2.5H = 390 ⇒ H = 156.Thus Hindi marks = 156 and Mathematics marks = 480 − 156 = 324.

Verification / Alternative check:
Check the condition: (1/3)*324 = 108 and (1/2)*156 = 78; 108 − 78 = 30, which matches the statement. Sum 324 + 156 = 480 also matches.

Why Other Options Are Wrong:
200, 196, 294: In each case, either the sum with M would not be 480 or the “exceeds by 30” relation would fail.

Common Pitfalls:
Forgetting to multiply both sides when clearing fractions; mixing up which quantity “exceeds” the other; or adding instead of subtracting in the relation. Carefully convert words to symbols before solving.

Final Answer:
156