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A can work twice as fast as B. A and C together can work thrice as fast as B. If A, B and C complete a job in 30 days working together, in how many days can each of them complete the work?
- a)60, 120, 120
- b)50, 100, 120
- c)60, 100, 80
- d)40, 80, 100
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A can work twice as fast as B. A and C together can work thrice as fas...
A, B and C complete a job in 30 days working together,
⇒ 1/A + 1/B + 1/C = 1/30
A can work twice as fast as B,
⇒ 1/B = 1/2A
A and C together can work thrice as fast as B,
⇒ 1/B = 1/3(1/A + 1/C)
Solving,
⇒ 3/B = 1/A + 1/C
⇒ 3/B = 1/30 – 1/B
⇒ 1/B = 120
Then,
⇒ 1/A = 1/60
⇒ 1/C = 1/120
∴ A, B and C can complete work in 60, 120 and 120 days respectively.
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A can work twice as fast as B. A and C together can work thrice as fas...
To solve this problem, let's assume that B can complete the work in x days.
According to the given information:
- A can work twice as fast as B, so A can complete the work in x/2 days.
- A and C together can work thrice as fast as B, so A and C together can complete the work in x/3 days.
Now, let's calculate the individual work rates of A, B, and C in terms of the work done per day.
- The work rate of A is 1/x/2 = 2/x (work done per day).
- The work rate of B is 1/x (work done per day).
- The work rate of A and C together is 1/x/3 = 3/x (work done per day).
Since A, B, and C are working together to complete the job in 30 days, their combined work rate is 1/30 (work done per day).
Now, we can set up an equation to solve for x, the number of days it takes for B to complete the work:
2/x + 1/x + 3/x = 1/30
Combining the terms with the same denominator on the left side of the equation, we get:
6/x = 1/30
Cross-multiplying, we get:
6 * 30 = x
x = 180
Therefore, B can complete the work in 180 days.
Substituting this value back into the individual work rates, we get:
- A can complete the work in x/2 = 180/2 = 90 days.
- C can complete the work in x/3 = 180/3 = 60 days.
So, the answer is option A: 60 days for A, 120 days for B, and 120 days for C.
According to the given information:
- A can work twice as fast as B, so A can complete the work in x/2 days.
- A and C together can work thrice as fast as B, so A and C together can complete the work in x/3 days.
Now, let's calculate the individual work rates of A, B, and C in terms of the work done per day.
- The work rate of A is 1/x/2 = 2/x (work done per day).
- The work rate of B is 1/x (work done per day).
- The work rate of A and C together is 1/x/3 = 3/x (work done per day).
Since A, B, and C are working together to complete the job in 30 days, their combined work rate is 1/30 (work done per day).
Now, we can set up an equation to solve for x, the number of days it takes for B to complete the work:
2/x + 1/x + 3/x = 1/30
Combining the terms with the same denominator on the left side of the equation, we get:
6/x = 1/30
Cross-multiplying, we get:
6 * 30 = x
x = 180
Therefore, B can complete the work in 180 days.
Substituting this value back into the individual work rates, we get:
- A can complete the work in x/2 = 180/2 = 90 days.
- C can complete the work in x/3 = 180/3 = 60 days.
So, the answer is option A: 60 days for A, 120 days for B, and 120 days for C.
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A can work twice as fast as B. A and C together can work thrice as fast as B. If A, B and C complete a job in 30 days working together, in how many days can each of them complete the work?a)60, 120, 120b)50, 100, 120c)60, 100, 80d)40, 80, 100Correct answer is option 'A'. Can you explain this answer?
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