Introduction / Context:
This question illustrates how ratios can represent comparisons between two exam scores. By combining the ratio with an absolute difference, we form a simple linear equation. Such questions test the ability to convert word statements into algebraic expressions and solve them systematically, which is a core skill in quantitative aptitude.
Given Data / Assumptions:
- Marks in English : marks in Hindi = 7 : 11.
- Marks in Hindi are 20 more than marks in English.
- We need to find Sanjay’s marks in English.
Concept / Approach:
Let us denote the common multiplying factor of the ratio by k, so that English marks and Hindi marks become 7k and 11k respectively. The problem states that Hindi marks exceed English marks by 20. This gives an equation involving k. Solving that equation provides the value of k, from which we can find the individual marks in each subject.
Step-by-Step Solution:
1) Let Sanjay’s marks in English be 7k and in Hindi be 11k.
2) According to the question, Hindi marks are 20 higher than English marks.
3) Therefore, 11k - 7k = 20.
4) Simplify the left side: 4k = 20.
5) Solve for k: k = 20 / 4 = 5.
6) English marks = 7k = 7 * 5 = 35.
7) Hindi marks = 11k = 11 * 5 = 55.
Verification / Alternative check:
We verify both the ratio and the difference condition. First, check the ratio: 35 : 55 simplifies by dividing both numbers by 5 to 7 : 11, which matches the given ratio. Second, check the difference: Hindi minus English = 55 - 35 = 20, which also matches the given extra marks in Hindi. Since both conditions are satisfied, our solution is consistent and correct.
Why Other Options Are Wrong:
Option B (55) is the Hindi score, not the English score. Options C (45), D (65) and E (40) do not yield the ratio 7 : 11 with a difference of 20 when paired with some corresponding Hindi marks. For example, if English were 45, then Hindi would be 65 to maintain a difference of 20, but 45 : 65 does not reduce to 7 : 11. Therefore, only 35 fits both the ratio and the difference conditions.
Common Pitfalls:
A common mistake is to confuse the direction of the difference and write English minus Hindi equals 20, or to add 20 to the wrong subject. Another typical error is trying to guess numbers without using the ratio method, which may lead to inconsistent pairs that do not satisfy both conditions. Always express the ratio using a variable multiplier, set up the difference equation carefully, and solve step by step.
Final Answer:
Sanjay’s marks in English are
35.
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