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A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
- a)10 days
- b)20 days
- c)5 days
- d)4 days
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A can do a piece of work in 4 days. B can do it in 5 days. With the as...
Understanding the Problem
To determine how many days C can complete the work alone, we first need to calculate the work rates of A, B, and C.
Work Rates of A and B
- A can complete the work in 4 days, so A's work rate is 1/4 of the work per day.
- B can complete the work in 5 days, so B's work rate is 1/5 of the work per day.
Combined Work Rate of A and B
- The combined work rate of A and B is:
- (1/4) + (1/5) = 5/20 + 4/20 = 9/20
This means A and B together can complete 9/20 of the work in one day.
Work Completed with C's Assistance
- Together, A, B, and C completed the work in 2 days. Thus, their combined work rate is:
- 1 total work / 2 days = 1/2 of the work per day.
Finding C's Work Rate
- Since A and B together do 9/20 of the work in a day, we set up the equation:
- (Work rate of A + Work rate of B + Work rate of C) = 1/2
- (9/20 + Work rate of C) = 1/2
To find C's work rate, we convert 1/2 to a common denominator:
- 1/2 = 10/20
Now we can solve for C's work rate:
- 9/20 + Work rate of C = 10/20
- Work rate of C = 10/20 - 9/20 = 1/20
Calculating C's Time to Complete the Work Alone
- If C's work rate is 1/20 of the work per day, C can complete the entire work alone in:
- 1 / (1/20) = 20 days.
Thus, the answer is that C alone can do the work in 20 days.
Correct Answer
- The correct option is (b) 20 days.
To determine how many days C can complete the work alone, we first need to calculate the work rates of A, B, and C.
Work Rates of A and B
- A can complete the work in 4 days, so A's work rate is 1/4 of the work per day.
- B can complete the work in 5 days, so B's work rate is 1/5 of the work per day.
Combined Work Rate of A and B
- The combined work rate of A and B is:
- (1/4) + (1/5) = 5/20 + 4/20 = 9/20
This means A and B together can complete 9/20 of the work in one day.
Work Completed with C's Assistance
- Together, A, B, and C completed the work in 2 days. Thus, their combined work rate is:
- 1 total work / 2 days = 1/2 of the work per day.
Finding C's Work Rate
- Since A and B together do 9/20 of the work in a day, we set up the equation:
- (Work rate of A + Work rate of B + Work rate of C) = 1/2
- (9/20 + Work rate of C) = 1/2
To find C's work rate, we convert 1/2 to a common denominator:
- 1/2 = 10/20
Now we can solve for C's work rate:
- 9/20 + Work rate of C = 10/20
- Work rate of C = 10/20 - 9/20 = 1/20
Calculating C's Time to Complete the Work Alone
- If C's work rate is 1/20 of the work per day, C can complete the entire work alone in:
- 1 / (1/20) = 20 days.
Thus, the answer is that C alone can do the work in 20 days.
Correct Answer
- The correct option is (b) 20 days.
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A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?a)10 daysb)20 daysc)5 daysd)4 daysCorrect answer is option 'B'. Can you explain this answer?
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