Income split and total constraint: Bina’s monthly income is 90% of Anita’s monthly income. The sum of their monthly incomes equals Mr. Sen’s monthly income. Mr. Sen’s annual income is ₹7,75,200. Find Bina’s monthly income.
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A₹ 34000
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B₹ 36000
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C₹ 30600
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D₹ 30000
Answer
Correct Answer: ₹ 30600
Explanation
Introduction / Context:We relate three incomes: two individual monthly incomes whose sum equals a third person’s monthly income. The third person’s annual income is provided, so first convert it to monthly, then allocate between Anita and Bina according to the 90% relation.Given Data / Assumptions:
- Mr. Sen’s annual income = ₹7,75,200 ⇒ monthly = 7,75,200 / 12 = ₹64,600.
- Bina = 90% of Anita ⇒ B = 0.9A.
- A + B = 64,600.
Concept / Approach:Express B in terms of A and substitute into the sum to solve for A. Then compute B = 0.9A. This is a basic linear equation in one variable after substitution.
Step-by-Step Solution:
A + 0.9A = 64,600 ⇒ 1.9A = 64,600.A = 64,600 / 1.9 = 34,000.B = 0.9A = 0.9 * 34,000 = ₹30,600.Verification / Alternative check:Sum check: 34,000 + 30,600 = 64,600 equals Mr. Sen’s monthly income; annualizing 64,600 * 12 = 7,75,200 as given.
Why Other Options Are Wrong:
- ₹34,000 and ₹36,000: These are Anita’s or unrelated values, not Bina’s monthly income.
- ₹30,000: Slight underestimate; 90% of 34,000 is exactly ₹30,600.
Common Pitfalls:Forgetting to convert annual to monthly, or misapplying the 90% to the combined income rather than to Anita’s income alone.
Final Answer:
₹ 30600