Difficulty: Medium
Correct Answer: 64,000
Explanation:
Introduction / Context:
This problem connects the salaries of three people using percentage relationships. It tests your ability to express different salaries in terms of one variable, convert an annual salary to a monthly salary and then backtrack to the unknown.
Given Data / Assumptions:
Concept / Approach:
We write the percentage relationships as equations. Using Vipin annual income, we deduce his monthly salary, from which we get Nikitha salary using the four fifths relation. Then we use the equality of 20% of K and 32% of N to find K.
Step-by-Step Solution:
Step 1: Convert Vipin annual salary to monthly: 3,84,000 / 12 = 32,000. So V = 32,000.Step 2: V is four fifths of N, so V = (4/5)N.Step 3: Hence N = V * (5/4) = 32,000 * (5/4) = 32,000 * 1.25 = 40,000.Step 4: Twenty percent of K equals thirty two percent of N.Step 5: Write this as 0.20K = 0.32N.Step 6: Substitute N = 40,000: 0.20K = 0.32 * 40,000 = 12,800.Step 7: So K = 12,800 / 0.20 = 64,000.
Verification / Alternative check:
Check the internal consistency. Twenty percent of 64,000 is 12,800. Thirty two percent of 40,000 is also 12,800, so the first relation holds. Four fifths of 40,000 is 32,000, matching Vipin monthly salary. Annual pay for Vipin is 32,000 * 12 = 3,84,000, as given.
Why Other Options Are Wrong:
Values 32,000, 40,000 and 52,000 fail to satisfy the equation 0.20K = 0.32N with N fixed at 40,000. They arise from misinterpreting which salary is larger or mixing up fractions.
Common Pitfalls:
Some students apply 20% and 32% to the wrong person or forget to convert Vipin annual salary correctly. Another frequent issue is solving the equation as 0.20K = 32N instead of 0.32N, which drastically changes the result.
Final Answer:
Karthik monthly salary is Rs. 64,000.
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