The average monthly income of P and Q is Rs. 5050, Q and R is Rs. 6250, and P and R is Rs. 5200. What is P's monthly income____________?
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Answer: B. Rs. 4000
Explanation
Summing the paired averages gives total sums of ten thousand one hundred, twelve thousand five hundred, and ten thousand four hundred. Adding all three pairs together yields twice the combined sum of all three individuals, totaling thirty-three thousand. Subtracting the combined sum of Q and R from the total sum of all three workers isolates P's monthly income at four thousand. Simultaneous equations involving paired averages can be solved by summing all equations to find the total combined value. Monthly income averages represent the mathematical mean of two individual salaries combined. Isolating a single variable from a three-variable sum requires subtracting the complementary pair total.
Option A underestimates P's income when tested against the paired average totals given in the problem. Option C fails to satisfy the exact subtraction balance required between the combined sums. Option D overestimates P's income by leaving insufficient remainder for the other two participants.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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