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A alone can complete work in 20 days and B alone can complete work in 30 days, C alone can complete work in 60 days. If A and B work for first day and B and C work for second day then how much time it will take for A, B and C together to complete the work after 2nd day?
- a)26/3 days
- b)30/13 days
- c)32/3 days
- d)13/15 days
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A alone can complete work in 20 days and B alone can complete work in ...
Given,
⇒ A’s 1 day’s work = 1/20
⇒ B’s 1 day’s work = 1/30
⇒ C’s 1 day’s work = 1/60
(A + B)’s 1 day’s work = 1/20 + 1/30
= 1/12
(B + C)’s 1 day’s work = 1/30 + 1/60
= 1/20
(A + B + C)’s 1 day’s work
= 1/20 + 1/30 + 1/60
= 1/10
Then,
Total work done till end of 2nd day
= 1/12 + 1/20
= 2/15
Remaining fraction of work
= 1 - 2/15
= 13/15
Total time taken by A, B and C together to complete work
= (13/15) × 10
= 26/3
It will take 26/3 days to complete remaining work.
⇒ A’s 1 day’s work = 1/20
⇒ B’s 1 day’s work = 1/30
⇒ C’s 1 day’s work = 1/60
(A + B)’s 1 day’s work = 1/20 + 1/30
= 1/12
(B + C)’s 1 day’s work = 1/30 + 1/60
= 1/20
(A + B + C)’s 1 day’s work
= 1/20 + 1/30 + 1/60
= 1/10
Then,
Total work done till end of 2nd day
= 1/12 + 1/20
= 2/15
Remaining fraction of work
= 1 - 2/15
= 13/15
Total time taken by A, B and C together to complete work
= (13/15) × 10
= 26/3
It will take 26/3 days to complete remaining work.
Most Upvoted Answer
A alone can complete work in 20 days and B alone can complete work in ...
Understanding Work Rates
To solve the problem, we first need to determine the work rates of A, B, and C.
- A's work rate: A can complete the work in 20 days.
- Work rate of A = 1/20 of the work per day.
- B's work rate: B can complete the work in 30 days.
- Work rate of B = 1/30 of the work per day.
- C's work rate: C can complete the work in 60 days.
- Work rate of C = 1/60 of the work per day.
Work Done in the First Two Days
Now, we will calculate the amount of work done on the first two days.
- **Day 1 (A and B working together)**:
- Work done = (1/20 + 1/30) = (3/60 + 2/60) = 5/60 = 1/12 of the work.
- **Day 2 (B and C working together)**:
- Work done = (1/30 + 1/60) = (2/60 + 1/60) = 3/60 = 1/20 of the work.
Total Work Done in 2 Days
Now, we sum the work done over the two days:
- Total work done in 2 days = 1/12 + 1/20
To add these fractions:
- LCM of 12 and 20 = 60
- Convert to a common denominator:
- 1/12 = 5/60
- 1/20 = 3/60
- Total = (5/60 + 3/60) = 8/60 = 2/15 of the work.
Remaining Work
Total work is 1, so remaining work after 2 days is:
- Remaining Work = 1 - 2/15 = 13/15 of the work.
Work Rate of A, B, and C Together
Now, we calculate the combined work rate of A, B, and C:
- A + B + C = (1/20 + 1/30 + 1/60)
- LCM of 20, 30, and 60 = 60
- Work rate = (3/60 + 2/60 + 1/60) = 6/60 = 1/10 of the work per day.
Time to Complete Remaining Work
Finally, to find the time required to finish the remaining 13/15 of the work:
- Time = Remaining Work / Work Rate = (13/15) / (1/10) = (13/15) * (10/1) = 130/15 = 26/3 days.
Thus, the time required for A, B, and C together to complete the work after the 2nd day is **26/3 days**.
**Correct answer: Option A.**
To solve the problem, we first need to determine the work rates of A, B, and C.
- A's work rate: A can complete the work in 20 days.
- Work rate of A = 1/20 of the work per day.
- B's work rate: B can complete the work in 30 days.
- Work rate of B = 1/30 of the work per day.
- C's work rate: C can complete the work in 60 days.
- Work rate of C = 1/60 of the work per day.
Work Done in the First Two Days
Now, we will calculate the amount of work done on the first two days.
- **Day 1 (A and B working together)**:
- Work done = (1/20 + 1/30) = (3/60 + 2/60) = 5/60 = 1/12 of the work.
- **Day 2 (B and C working together)**:
- Work done = (1/30 + 1/60) = (2/60 + 1/60) = 3/60 = 1/20 of the work.
Total Work Done in 2 Days
Now, we sum the work done over the two days:
- Total work done in 2 days = 1/12 + 1/20
To add these fractions:
- LCM of 12 and 20 = 60
- Convert to a common denominator:
- 1/12 = 5/60
- 1/20 = 3/60
- Total = (5/60 + 3/60) = 8/60 = 2/15 of the work.
Remaining Work
Total work is 1, so remaining work after 2 days is:
- Remaining Work = 1 - 2/15 = 13/15 of the work.
Work Rate of A, B, and C Together
Now, we calculate the combined work rate of A, B, and C:
- A + B + C = (1/20 + 1/30 + 1/60)
- LCM of 20, 30, and 60 = 60
- Work rate = (3/60 + 2/60 + 1/60) = 6/60 = 1/10 of the work per day.
Time to Complete Remaining Work
Finally, to find the time required to finish the remaining 13/15 of the work:
- Time = Remaining Work / Work Rate = (13/15) / (1/10) = (13/15) * (10/1) = 130/15 = 26/3 days.
Thus, the time required for A, B, and C together to complete the work after the 2nd day is **26/3 days**.
**Correct answer: Option A.**
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