Difficulty: Medium
Correct Answer: 33
Explanation:
Introduction / Context:
This is a percentage and algebra problem involving two related scores. It tests the ability to translate verbal conditions into algebraic equations and then solve for one of the unknowns using percentage information.
Given Data / Assumptions:
Concept / Approach:
Let Geography marks be G and History marks be G + 9. The sum of the marks is (G + 9) + G = 2G + 9. The percentage condition says that History marks equal 56 percent of this sum. We form an equation based on this and solve for G.
Step-by-Step Solution:
Let Geography marks = G.Then History marks = G + 9.Sum of marks = G + 9 + G = 2G + 9.Given that History marks = 56 percent of sum.So G + 9 = 0.56 * (2G + 9).Write 0.56 as 56 / 100 = 14 / 25 for exact arithmetic.Thus G + 9 = (14 / 25) * (2G + 9).Multiply both sides by 25: 25G + 225 = 14(2G + 9) = 28G + 126.Rearrange: 25G + 225 = 28G + 126 → 225 - 126 = 28G - 25G.So 99 = 3G and G = 33.
Verification / Alternative check:
If Geography marks are 33, History marks are 33 + 9 = 42. Sum is 33 + 42 = 75. Check the percentage: 56 percent of 75 = 0.56 * 75 = 42, which exactly equals the History marks, confirming the solution.
Why Other Options Are Wrong:
Values 42, 65 and 53 do not satisfy the condition that History marks are 9 more than Geography marks and at the same time 56 percent of the sum. Substituting any of them for G fails the equation G + 9 = 0.56(2G + 9).
Common Pitfalls:
Common mistakes include mixing up which subject has the higher marks or incorrectly forming the percentage equation, for example taking 56 percent of only one subject. It is crucial to define variables clearly and express all conditions algebraically before solving.
Final Answer:
Priya's Geography marks are 33.
Discussion & Comments