Vinay scored thrice as many marks in Mathematics as in English. The proportion of his marks in Mathematics and History is 4 : 3. If his total marks in Mathematics, English, and History is 250, what are his marks in English?

Introduction / Context:
This marks-allocation problem uses two relationships: a direct multiple between Mathematics and English, and a ratio between Mathematics and History. We then apply the total-sum constraint to solve for each subject’s marks.

Given Data / Assumptions:

• Maths = 3 * English.
• Maths : History = 4 : 3.
• Total of Maths + English + History = 250.

Concept / Approach:
Let English = x ⇒ Maths = 3x. From Maths : History = 4 : 3, History = (3/4)*Maths = (3/4)*3x = 9x/4. Sum the three expressions and set equal to 250, then solve for x.

Step-by-Step Solution:
Let E = x, M = 3x, H = 9x/4. Total: x + 3x + 9x/4 = 250. Combine: (4x + 12x + 9x)/4 = 25x/4 = 250. 25x = 1000 ⇒ x = 40. English = 40.

Verification / Alternative check:
Maths = 120; History = 90. Sum = 40 + 120 + 90 = 250, consistent.

Why Other Options Are Wrong:
120 and 90 correspond to Maths and History, not English. 80 is not consistent with the given relationships.

Common Pitfalls:
Mixing up which subject is a multiple of which, or misapplying the 4 : 3 ratio. Always define variables clearly and substitute carefully.

Final Answer:
40