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L alone can do a work in 30 days. M alone can do the same in 45 days. L, M and N together can do the same work in 9 days. In how many days can N alone do the work?
- a)19
- b)20
- c)18
- d)22
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
L alone can do a work in 30 days. M alone can do the same in 45 days. ...
Work done by L in one day = 1/30
Work done by M in one day = 1/45
Work done by L, M and N together in one day = 1/9
Work done by L and M together in one day = (1/30) + (1/45) = 1/18
Work done by N alone in one day = (1/9) – (1/18) = 1/18
Time taken by N alone to do the work = 1/(1/18) = 18 days
∴ Time taken by N alone to do the work = 18 days
Work done by M in one day = 1/45
Work done by L, M and N together in one day = 1/9
Work done by L and M together in one day = (1/30) + (1/45) = 1/18
Work done by N alone in one day = (1/9) – (1/18) = 1/18
Time taken by N alone to do the work = 1/(1/18) = 18 days
∴ Time taken by N alone to do the work = 18 days
Most Upvoted Answer
L alone can do a work in 30 days. M alone can do the same in 45 days. ...
Given Information:
- L can complete the work in 30 days
- M can complete the work in 45 days
- L, M, and N together can complete the work in 9 days
Calculation:
Let's assume the total work to be done is 90 units (LCM of 30, 45, and 9).
- L's work rate = 90/30 = 3 units/day
- M's work rate = 90/45 = 2 units/day
- L, M, and N's combined work rate = 90/9 = 10 units/day
Now, we can calculate N's work rate:
- L, M, and N's combined work rate = L's work rate + M's work rate + N's work rate
- 10 units/day = 3 units/day + 2 units/day + N's work rate
- N's work rate = 10 - 3 - 2 = 5 units/day
Final Calculation:
To find out how many days N alone can complete the work, we divide the total work (90 units) by N's work rate:
- N's time to complete the work = 90 units / 5 units/day = 18 days
Therefore, N alone can complete the work in 18 days. Hence, the correct answer is option 'C'.
- L can complete the work in 30 days
- M can complete the work in 45 days
- L, M, and N together can complete the work in 9 days
Calculation:
Let's assume the total work to be done is 90 units (LCM of 30, 45, and 9).
- L's work rate = 90/30 = 3 units/day
- M's work rate = 90/45 = 2 units/day
- L, M, and N's combined work rate = 90/9 = 10 units/day
Now, we can calculate N's work rate:
- L, M, and N's combined work rate = L's work rate + M's work rate + N's work rate
- 10 units/day = 3 units/day + 2 units/day + N's work rate
- N's work rate = 10 - 3 - 2 = 5 units/day
Final Calculation:
To find out how many days N alone can complete the work, we divide the total work (90 units) by N's work rate:
- N's time to complete the work = 90 units / 5 units/day = 18 days
Therefore, N alone can complete the work in 18 days. Hence, the correct answer is option 'C'.
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L alone can do a work in 30 days. M alone can do the same in 45 days. L, M and N together can do the same work in 9 days. In how many days can N alone do the work?a)19b)20c)18d)22Correct answer is option 'C'. Can you explain this answer?
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