Rs. 1200 is divided among P, Q, and R. P receives half of Q and R's combined total, while Q receives one-third of P and R's combined total. Find R's amount?
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Answer: B. Rs.500
Explanation
Translating the given proportional relationships into a system of linear equations links all three shares together. Solving the simultaneous equations using the total sum of twelve hundred rupees isolates individual amounts. Calculating the specific value assigned to the final variable reveals that R receives five hundred rupees. Simultaneous linear equations allow solvers to determine unknown variables from multiple interconnected constraints. Splitting a total amount among multiple parties requires ensuring all individual shares add up to the total. Algebraic substitution is a reliable method for solving multi-variable financial distribution problems.
Business partners divide profits using proportional formulas similar to this multi-party allocation puzzle. Estate executors rely on precise mathematical equations to distribute inheritance funds among beneficiaries. Mastering simultaneous equations builds critical thinking skills for advanced algebraic applications. Option A underestimates R's financial share by miscalculating the simultaneous equation coefficients. Option C results from an arithmetic error during the final variable isolation step. Option D overestimates the allocated share, violating the total sum constraint of twelve hundred rupees.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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