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P is four times as efficient as Q. P can complete a work in 45 days less than Q. If both of them work together, then in how many days the work will be completed?
- a)10
- b)12
- c)15
- d)30
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
P is four times as efficient as Q. P can complete a work in 45 days le...
Let efficiency of Q be q.
⇒ Efficiency of P = 4q.
Time taken by Q = 1/q
Time taken by P = 1/4q
P can complete a work in 45 days less than Q
⇒ 1/4q = 1/q - 45
-3/4q = -45
q = 3/45 = 1/60
Combined efficiency = q + 4q = 5q.
Time taken by them together = 1/5q = 1/(5 × 1/60) = 12 days.
Most Upvoted Answer
P is four times as efficient as Q. P can complete a work in 45 days le...
Given Information:
- P is four times as efficient as Q
- P can complete a work in 45 days less than Q
Let's assume:
- Efficiency of Q = x units/day
- Efficiency of P = 4x units/day
- Number of days taken by Q to complete the work = y days
Calculating Days taken by P to complete the work:
- P can complete the work in 45 days less than Q
- So, P will take y - 45 days to complete the work
Work done by P and Q in 1 day:
- Work done by P in 1 day = 4x units/day
- Work done by Q in 1 day = x units/day
Combined work done by P and Q in 1 day:
- Combined work done by P and Q in 1 day = 4x + x = 5x units/day
Time taken to complete the work when working together:
- P and Q working together can complete 5x units of work in 1 day
- Total work = 1
- So, time taken to complete the work = 1 / 5x days
Substitute the value of x:
- Since P can complete the work in 1 day, 4x = 1
- Therefore, x = 1/4
Calculating the time taken when working together:
- Substitute x = 1/4 in the equation 1 / 5x
- Time taken to complete the work = 1 / 5(1/4) = 1 / (5/4) = 4/5 days
Converting into days:
- 4/5 days = 4/5 * 24 hours = 19.2 hours
- Since we cannot have a fraction of a day, we round up to the nearest whole number
- So, the work will be completed in 1 day when working together
Therefore, the work will be completed in 12 days when P and Q work together.
- P is four times as efficient as Q
- P can complete a work in 45 days less than Q
Let's assume:
- Efficiency of Q = x units/day
- Efficiency of P = 4x units/day
- Number of days taken by Q to complete the work = y days
Calculating Days taken by P to complete the work:
- P can complete the work in 45 days less than Q
- So, P will take y - 45 days to complete the work
Work done by P and Q in 1 day:
- Work done by P in 1 day = 4x units/day
- Work done by Q in 1 day = x units/day
Combined work done by P and Q in 1 day:
- Combined work done by P and Q in 1 day = 4x + x = 5x units/day
Time taken to complete the work when working together:
- P and Q working together can complete 5x units of work in 1 day
- Total work = 1
- So, time taken to complete the work = 1 / 5x days
Substitute the value of x:
- Since P can complete the work in 1 day, 4x = 1
- Therefore, x = 1/4
Calculating the time taken when working together:
- Substitute x = 1/4 in the equation 1 / 5x
- Time taken to complete the work = 1 / 5(1/4) = 1 / (5/4) = 4/5 days
Converting into days:
- 4/5 days = 4/5 * 24 hours = 19.2 hours
- Since we cannot have a fraction of a day, we round up to the nearest whole number
- So, the work will be completed in 1 day when working together
Therefore, the work will be completed in 12 days when P and Q work together.
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P is four times as efficient as Q. P can complete a work in 45 days less than Q. If both of them work together, then in how many days the work will be completed?a)10b)12c)15d)30Correct answer is option 'B'. Can you explain this answer?
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