Math Problem Statement
Q4.Time taken by A to finish a piece of work is twice the time taken B and thrice the time taken by C. If all three of them work together, it takes them 2 days to complete the entire work. How much work was done by B alone?
2 days
6 days
3 days
5 days
Cannot be determined
Solution
Let the time taken by B to finish the work be days.
- A takes twice as much time as B, so A's time is days.
- C takes one-third of the time as A, which means C's time is days.
The work done by each individual in one day is the reciprocal of the time they take to complete the work.
- Work done by A in 1 day =
- Work done by B in 1 day =
- Work done by C in 1 day =
Since all three work together, their combined rate is:
It is given that they complete the entire work in 2 days. Therefore:
Solving for :
Thus, B alone can complete the entire work in 6 days.
Therefore, the correct answer is 6 days.
Do you need more details or have any questions?
Here are some related questions for practice:
- If B alone works for 1 day, how much of the work will be completed?
- How long will it take A and C to complete the work if B doesn't participate?
- What is the total work done by C in 2 days?
- If B and C work together, how long will it take them to complete the work?
- How much work does A do in 1 day if B alone takes 6 days?
Tip: When solving work-rate problems, always remember that individual work rates can be added together when multiple workers are working simultaneously.
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Math Problem Analysis
Mathematical Concepts
Work and Time Problems
Ratio and Proportion
Formulas
Work done = Rate × Time
Combined work rate = Sum of individual work rates
Theorems
Work-rate theorem: The combined work rate is the sum of individual rates.
Suitable Grade Level
Grades 9-10
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