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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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