Math Problem Statement
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Solution
Let’s break down the problem step by step.
Step 1: Calculate A and B's individual work rates
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A can complete the work in 6 days, so A’s work rate is:
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B can complete the work in 8 days, so B’s work rate is:
Step 2: Calculate the combined work rate of A, B, and C
- A, B, and C together completed the work in 3 days. Therefore, the combined work rate of A, B, and C is:
Since A and B together can complete the work in:
Thus, the rate of C’s work is: Let’s calculate that: Therefore, C's work rate is of the work per day.
Step 3: Determine the payment for C
- The total payment for completing the work is Rs. 3200.
- Since C’s work rate is , C completed of the work.
- The amount C should be paid is:
Thus, C should be paid Rs. 133.33.
Would you like a more detailed explanation of any step? Or do you have any other questions?
Here are some related questions you might find helpful:
- How to calculate combined work rates of two or more people?
- What is the method to determine individual payments in joint work problems?
- How do you deal with fractions of work and rates in real-world problems?
- How can you solve similar work problems involving different time frames?
- How do you approach rate-based work problems when multiple workers are involved?
Tip: When solving work-rate problems, always ensure to express the rate of each person in the same unit (work/day or work/hour) to avoid mistakes.
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Math Problem Analysis
Mathematical Concepts
Work and Time
Rates of Work
Fractional Work
Formulas
Rate of Work = 1 / Time
Combined Rate = Rate of A + Rate of B + Rate of C
Payment = Work fraction completed by C * Total Payment
Theorems
Work-rate Theorem
Work Completion Theorem
Suitable Grade Level
Grades 7-9