Math Problem Statement
Mahesh and Suresh can complete a work in 16 days and 12 days, respectively. Starting with Mahesh, they work on alternate basis. How many days will take to finalise the complete work? Ans 1.
Solution
To determine how many days it will take Mahesh and Suresh to complete the work when they alternate working days, we need to find their combined work rate and then determine how many days it will take them together.
Given:
- Mahesh can complete the work in 16 days.
- Suresh can complete the work in 12 days.
First, we find the work rates:
- Mahesh's work rate is of the work per day.
- Suresh's work rate is of the work per day.
When they work alternately, let's analyze the work done in two days:
- Day 1: Mahesh works of the work.
- Day 2: Suresh works of the work.
The total work done in two days is:
To combine these rates, we need a common denominator:
Adding these fractions:
So, in two days, they complete of the work.
Next, we need to determine how many full cycles (of two days each) are needed to get close to completing the work.
Since one cycle of two days completes of the work, the number of cycles needed to get close to 1 (the entire work) can be found by dividing 1 by :
This means 6 full cycles will complete:
After 6 cycles (12 days), of the work is done. The remaining work is:
On the 13th day, Mahesh will work and he completes of the work per day. Therefore, to finish the remaining of the work:
This means Mahesh will need 2 additional days to complete the remaining work. So, the total number of days taken to finalize the complete work is:
Thus, the correct answer is:
14 days
Would you like further details or have any questions?
Here are 5 questions you might want to ask:
- How do you calculate work rates for multiple workers?
- What is the concept of alternate work in shared tasks?
- Can you provide more examples of work problems involving multiple workers?
- How do you handle fractional work rates?
- What are some tips for solving time and work problems efficiently?
Tip: When solving work problems involving alternating tasks, always consider the combined work rate and analyze how many cycles are needed to complete the task.
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Math Problem Analysis
Mathematical Concepts
Work and Time Problems
Alternate Work
Fractional Work Rates
Formulas
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Theorems
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Suitable Grade Level
High School
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