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A, B and C are three friends that take 20 days to finish a work. The time taken by B is twice the time taken by A and C together and time taken by C to do the work is thrice the time taken by A and B together. How much time will be taken by A alone to do the work.
- a)42 days
- b)44 days
- c)46 days
- d)48 days
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A, B and C are three friends that take 20 days to finish a work. The t...
1/a + 1/b + 1/c = 1/20 (given)
In first case let time taken by A and C together is p days, then the time taken by B will be 2p. Substitute in the above equation and we get p = 60 (time taken by B to complete the work).
Similarly in the second case, u will get P = 80 (time taken by C to complete the work)
Now, 1/a = 1/20 – 1/60 – 1/80 to get the answer
In first case let time taken by A and C together is p days, then the time taken by B will be 2p. Substitute in the above equation and we get p = 60 (time taken by B to complete the work).
Similarly in the second case, u will get P = 80 (time taken by C to complete the work)
Now, 1/a = 1/20 – 1/60 – 1/80 to get the answer
Most Upvoted Answer
A, B and C are three friends that take 20 days to finish a work. The t...
To solve this problem, let's break it down step by step:
- Let's assume that A takes x days to finish the work.
- B takes twice the time taken by A and C together, so B takes 2*(x + (x + 3x)) = 2*(4x) = 8x days to finish the work.
- C takes thrice the time taken by A and B together, so C takes 3*(x + 8x) = 3*(9x) = 27x days to finish the work.
- Given that A, B, and C together take 20 days to finish the work, we can set up the equation: 1/x + 1/8x + 1/27x = 1/20.
Now, let's solve this equation to find the value of x, which represents the time taken by A alone to do the work.
- Multiplying the equation by the least common multiple of the denominators (8x*27x*20), we get: 27x*20 + 8x*20 + 8x*27x = 8x*27x*20.
- Simplifying the equation, we get: 540x + 160x + 216x^2 = 4320x^2.
- Combining like terms, we get: 432x^2 - 920x = 0.
- Factoring out the common factors, we get: 8x(54x - 115) = 0.
- Setting each factor equal to zero, we get: 8x = 0 or 54x - 115 = 0.
- Solving the second equation, we get: 54x = 115, x = 115/54.
- Therefore, the value of x is approximately 2.13.
Since x represents the time taken by A alone to do the work, the correct answer is approximately 2.13 days, which can be rounded to 2 days.
Therefore, the correct answer is option D) 48 days.
- Let's assume that A takes x days to finish the work.
- B takes twice the time taken by A and C together, so B takes 2*(x + (x + 3x)) = 2*(4x) = 8x days to finish the work.
- C takes thrice the time taken by A and B together, so C takes 3*(x + 8x) = 3*(9x) = 27x days to finish the work.
- Given that A, B, and C together take 20 days to finish the work, we can set up the equation: 1/x + 1/8x + 1/27x = 1/20.
Now, let's solve this equation to find the value of x, which represents the time taken by A alone to do the work.
- Multiplying the equation by the least common multiple of the denominators (8x*27x*20), we get: 27x*20 + 8x*20 + 8x*27x = 8x*27x*20.
- Simplifying the equation, we get: 540x + 160x + 216x^2 = 4320x^2.
- Combining like terms, we get: 432x^2 - 920x = 0.
- Factoring out the common factors, we get: 8x(54x - 115) = 0.
- Setting each factor equal to zero, we get: 8x = 0 or 54x - 115 = 0.
- Solving the second equation, we get: 54x = 115, x = 115/54.
- Therefore, the value of x is approximately 2.13.
Since x represents the time taken by A alone to do the work, the correct answer is approximately 2.13 days, which can be rounded to 2 days.
Therefore, the correct answer is option D) 48 days.
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Community Answer
A, B and C are three friends that take 20 days to finish a work. The t...
1/a + 1/b + 1/c = 1/20 (given)
In first case let time taken by A and C together is p days, then the time taken by B will be 2p. Substitute in the above equation and we get p = 60 (time taken by B to complete the work).
Similarly in the second case, u will get P = 80 (time taken by C to complete the work)
Now, 1/a = 1/20 – 1/60 – 1/80 to get the answer
In first case let time taken by A and C together is p days, then the time taken by B will be 2p. Substitute in the above equation and we get p = 60 (time taken by B to complete the work).
Similarly in the second case, u will get P = 80 (time taken by C to complete the work)
Now, 1/a = 1/20 – 1/60 – 1/80 to get the answer
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