Priya's marks in History and Geography are in the ratio 5:7. If she scores 14 more marks in Geography than in History, what are her marks in History?

Introduction / Context:
This problem is a standard ratio and difference based aptitude question involving marks in two subjects. Such questions check whether the student can convert ratio information into algebraic expressions and then use the given numerical difference to find exact values. The focus is on understanding how a simple ratio translates into actual numerical scores when one extra condition is given.

Given Data / Assumptions:

Marks in History and Geography are in the ratio 5:7.
Geography marks exceed History marks by 14 marks.
Both marks are assumed to be non negative integers.
We are asked specifically for the marks in History.

Concept / Approach:
If two quantities are in the ratio a:b, we can represent them as a common multiple k such that first quantity = a * k and second quantity = b * k. The difference between them can then be written in terms of k. By equating this algebraic difference to the given numerical difference, we can solve for k and then find the actual values of both quantities. Finally, we pick the required one, which is the History marks.

Step-by-Step Solution:
Let Priya's History marks be 5k. Let Priya's Geography marks be 7k. Given that Geography exceeds History by 14 marks, so 7k - 5k = 14. Simplify: 2k = 14. Therefore k = 14 / 2 = 7. History marks = 5k = 5 * 7 = 35.

Verification / Alternative check:
Substitute k = 7 back into both expressions. Geography marks = 7 * 7 = 49, History marks = 35. The difference 49 - 35 equals 14, which matches the given condition. Also, the ratio 35:49 simplifies by dividing numerator and denominator by 7, giving 5:7, which confirms that both the ratio and the difference condition are satisfied simultaneously.

Why Other Options Are Wrong:
Option 49 corresponds to the Geography marks, not the History marks that the question asks for.
Option 42 would require a different ratio or difference, since 49 and 42 differ by 7, not 14, and the ratio 42:56 is not 5:7 for any consistent pair here.
Option 56 does not fit as History marks because then Geography would be 56 * 7 / 5 which is not an integer and would not keep the ratio exactly 5:7.

Common Pitfalls:
Students sometimes reverse the difference and set 5k - 7k = 14, which leads to negative values.
Another common error is to treat the ratio 5:7 as an actual pair of marks instead of a scaled relationship, ignoring the given difference of 14 entirely.
Some learners also mistakenly assume that the larger ratio number must correspond to the subject with the smaller given marks, which is incorrect here.

Final Answer:
Priya scores 35 marks in History.