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Manoj takes twice as much time as Anjay and thrice as much as Vijay to finish a piece of work.Together they finish the work in 1 day. What is the time taken by Manoj to finish the work?
- a)6 days
- b)3 days
- c)2 days
- d)4 days
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Manoj takes twice as much time as Anjay and thrice as much as Vijay to...
Let Anjay take 3t days, Vijay take 2t days and Manoj take 6t days in order to complete the work.
Then we get:
1/3t + 1/2t + 1/6t = 1 Æ t = 1. Thus, Manoj would take 6t = 6 days to complete the work.
Then we get:
1/3t + 1/2t + 1/6t = 1 Æ t = 1. Thus, Manoj would take 6t = 6 days to complete the work.
Most Upvoted Answer
Manoj takes twice as much time as Anjay and thrice as much as Vijay to...
Given information:
- Manoj takes twice as much time as Anjay to finish a piece of work.
- Manoj takes thrice as much time as Vijay to finish a piece of work.
- Together they finish the work in 1 day.
To find:
- The time taken by Manoj to finish the work.
Solution:
Let's assume that Vijay takes 'x' days to finish the work.
- Therefore, Anjay would take '2x' days to finish the work, as Manoj takes twice as much time as Anjay.
- And, Manoj would take '3x' days to finish the work, as Manoj takes thrice as much time as Vijay.
Now, let's calculate the combined work done by all three of them in a day:
- Vijay does 1/x of the work in a day.
- Anjay does 1/(2x) of the work in a day, as he takes twice as much time as Vijay.
- Manoj does 1/(3x) of the work in a day, as he takes thrice as much time as Vijay.
- So, the combined work done by all three of them in a day would be: 1/x + 1/(2x) + 1/(3x) = (6 + 3 + 2)/6x = 11/6x
As per the question, they finish the work in 1 day. Therefore, the combined work done by all three of them in a day would be equal to 1. Hence, we can write:
11/6x = 1
x = 11/6
- So, Vijay takes 11/6 days to finish the work.
- Anjay takes twice the time, i.e. 22/6 = 11/3 days to finish the work.
- Manoj takes thrice the time, i.e. 33/6 = 11/2 days to finish the work.
Therefore, the time taken by Manoj to finish the work is 11/2 days, which is option A.
- Manoj takes twice as much time as Anjay to finish a piece of work.
- Manoj takes thrice as much time as Vijay to finish a piece of work.
- Together they finish the work in 1 day.
To find:
- The time taken by Manoj to finish the work.
Solution:
Let's assume that Vijay takes 'x' days to finish the work.
- Therefore, Anjay would take '2x' days to finish the work, as Manoj takes twice as much time as Anjay.
- And, Manoj would take '3x' days to finish the work, as Manoj takes thrice as much time as Vijay.
Now, let's calculate the combined work done by all three of them in a day:
- Vijay does 1/x of the work in a day.
- Anjay does 1/(2x) of the work in a day, as he takes twice as much time as Vijay.
- Manoj does 1/(3x) of the work in a day, as he takes thrice as much time as Vijay.
- So, the combined work done by all three of them in a day would be: 1/x + 1/(2x) + 1/(3x) = (6 + 3 + 2)/6x = 11/6x
As per the question, they finish the work in 1 day. Therefore, the combined work done by all three of them in a day would be equal to 1. Hence, we can write:
11/6x = 1
x = 11/6
- So, Vijay takes 11/6 days to finish the work.
- Anjay takes twice the time, i.e. 22/6 = 11/3 days to finish the work.
- Manoj takes thrice the time, i.e. 33/6 = 11/2 days to finish the work.
Therefore, the time taken by Manoj to finish the work is 11/2 days, which is option A.
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