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A and B together can complete a piece of work in 15 days, B and C together can complete the work in 20 days. A and C together can complete the work in 30 days. What is the ratio of number of days A alone takes to do the work to the number of days C alone takes to do the work?
- a)1 : 6
- b)1 : 3
- c)2 : 3
- d)3 : 2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A and B together can complete a piece of work in 15 days, B and C toge...
Let A, B and C take a, b and c days respectively to complete the work.
=> 1/a + 1/b = 1/15 -> (1)
1/b + 1/c = 1/20 -> (2)
1/c + 1/a = 1/30 -> (3)
(1) - (2)
=> 1/a - 1/c = 1/15 - 1/20
=> 1/a - 1/c = (4-3)/60 = 1/60
∴ 1/a - 1/c = 1/30
1/a + 1/c = 1/30
----------------------
2/a = 1/60 + 1/30 = 1/20
∴ 1/a = 1/40 => a = 40
=> 1/c = 1/30 - 1/40 = (4-3)/120 = 1/120
=> c = 120
The required ratio = a : c
= 40 : 120 = 1 : 3 Choice (2)
Most Upvoted Answer
A and B together can complete a piece of work in 15 days, B and C toge...
Given Information:
- A + B = 1/15
- B + C = 1/20
- A + C = 1/30
Calculation:
Let's assume A alone takes x days to complete the work, and C alone takes y days to complete the work.
From the given information, we can find:
- A + B + C = (A + B) + (B + C) - (A + C) = 1/15 + 1/20 - 1/30
- A + B + C = (4 + 3 - 2) / 60
- A + B + C = 5 / 60
- A + B + C = 1/12
Therefore, A alone can complete the work in 12 days.
Similarly, we can find:
- B alone can complete the work in 20 days
- C alone can complete the work in 60 days
Ratio:
The ratio of the number of days A alone takes to do the work to the number of days C alone takes to do the work is:
- x:y = 12:60
- x:y = 1:5
Therefore, the required ratio is 1:5, which simplifies to 1:3. Hence, the correct answer is option B.
- A + B = 1/15
- B + C = 1/20
- A + C = 1/30
Calculation:
Let's assume A alone takes x days to complete the work, and C alone takes y days to complete the work.
From the given information, we can find:
- A + B + C = (A + B) + (B + C) - (A + C) = 1/15 + 1/20 - 1/30
- A + B + C = (4 + 3 - 2) / 60
- A + B + C = 5 / 60
- A + B + C = 1/12
Therefore, A alone can complete the work in 12 days.
Similarly, we can find:
- B alone can complete the work in 20 days
- C alone can complete the work in 60 days
Ratio:
The ratio of the number of days A alone takes to do the work to the number of days C alone takes to do the work is:
- x:y = 12:60
- x:y = 1:5
Therefore, the required ratio is 1:5, which simplifies to 1:3. Hence, the correct answer is option B.
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A and B together can complete a piece of work in 15 days, B and C together can complete the work in 20 days. A and C together can complete the work in 30 days. What is the ratio of number of days A alone takes to do the work to the number of days C alone takes to do the work?a)1 : 6b)1 : 3c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer?
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