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When Ashok and Karthik are working alone, they can complete a piece of work in 25 days and 30 days respectively. On day 1, Karthik started the work and Ashok joined B from day 3 on-wards. Find approximately after how many days will the work be completed?
- a)20 days
- b)10 days
- c)15 days
- d)25 days
- e)30 days
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
When Ashok and Karthik are working alone, they can complete a piece of...
Fraction of work completed by Karthik on day 1 and day 2 = 2* 1/30 = 1/15
Fraction of work left after 2 days = 14/15
Fraction of work completed by Both = 1/25 + 1/30 = 11/150
Number of days after day 2 to complete work = 14*150/15*11 = 13 days
So after 2+13 = 15 days works will be completed
Fraction of work left after 2 days = 14/15
Fraction of work completed by Both = 1/25 + 1/30 = 11/150
Number of days after day 2 to complete work = 14*150/15*11 = 13 days
So after 2+13 = 15 days works will be completed
Most Upvoted Answer
When Ashok and Karthik are working alone, they can complete a piece of...
**Given Information:**
- Ashok can complete a piece of work alone in 25 days.
- Karthik can complete a piece of work alone in 30 days.
- Karthik started the work alone on day 1.
- Ashok joined the work on day 3.
**Approach:**
- We need to find approximately after how many days the work will be completed.
- Let's assume the work will be completed in x days.
- We can calculate the fraction of work done by Karthik and Ashok in a day.
- Using this information, we can set up an equation to solve for x.
**Calculation:**
- Karthik can complete 1/30th of the work in a day.
- Ashok can complete 1/25th of the work in a day.
- From day 1 to day 2, Karthik completes 1/30th of the work.
- From day 3 onwards, both Karthik and Ashok work together.
**Work done by Karthik and Ashok from day 3 onwards:**
- From day 3 to day x, both Karthik and Ashok work together for (x - 2) days.
- Karthik completes (x - 2)/30th of the work in (x - 2) days.
- Ashok completes (x - 2)/25th of the work in (x - 2) days.
**Total work done:**
- The total work done by Karthik and Ashok should be equal to the entire work.
- Therefore, we can set up the equation:
1/30 + (x - 2)/30 + (x - 2)/25 = 1
**Solving the equation:**
- Multiply all terms by the least common multiple of the denominators (150):
5 + 5(x - 2) + 6(x - 2) = 150
5 + 5x - 10 + 6x - 12 = 150
11x - 17 = 150
- Simplify the equation:
11x = 150 + 17
11x = 167
- Divide both sides by 11:
x = 167/11
x ≈ 15.18
**Conclusion:**
- Therefore, approximately after 15 days, the work will be completed.
- The correct answer is option C.
- Ashok can complete a piece of work alone in 25 days.
- Karthik can complete a piece of work alone in 30 days.
- Karthik started the work alone on day 1.
- Ashok joined the work on day 3.
**Approach:**
- We need to find approximately after how many days the work will be completed.
- Let's assume the work will be completed in x days.
- We can calculate the fraction of work done by Karthik and Ashok in a day.
- Using this information, we can set up an equation to solve for x.
**Calculation:**
- Karthik can complete 1/30th of the work in a day.
- Ashok can complete 1/25th of the work in a day.
- From day 1 to day 2, Karthik completes 1/30th of the work.
- From day 3 onwards, both Karthik and Ashok work together.
**Work done by Karthik and Ashok from day 3 onwards:**
- From day 3 to day x, both Karthik and Ashok work together for (x - 2) days.
- Karthik completes (x - 2)/30th of the work in (x - 2) days.
- Ashok completes (x - 2)/25th of the work in (x - 2) days.
**Total work done:**
- The total work done by Karthik and Ashok should be equal to the entire work.
- Therefore, we can set up the equation:
1/30 + (x - 2)/30 + (x - 2)/25 = 1
**Solving the equation:**
- Multiply all terms by the least common multiple of the denominators (150):
5 + 5(x - 2) + 6(x - 2) = 150
5 + 5x - 10 + 6x - 12 = 150
11x - 17 = 150
- Simplify the equation:
11x = 150 + 17
11x = 167
- Divide both sides by 11:
x = 167/11
x ≈ 15.18
**Conclusion:**
- Therefore, approximately after 15 days, the work will be completed.
- The correct answer is option C.
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