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P and Q together can complete a piece of work in 8 days, Q alone can complete the same work in 12 days.In how many days can P alone complete the same work?
- a)24
- b)12
- c)18
- d)36
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
P and Q together can complete a piece of work in 8 days, Q alone can c...
Let total work = LCM of 8 and 12 = 24 units
Efficiency of P&Q; = 24/8 = 3
Efficiency of Q = 24/12 = 2
Then efficiency of P = 3-2 = 1
P alone can complete 24 units of work in 24/1 = 24 days
So the answer is option A.
Most Upvoted Answer
P and Q together can complete a piece of work in 8 days, Q alone can c...
Given:
P and Q together can complete a piece of work in 8 days.
Q alone can complete the same work in 12 days.
To find:
In how many days can P alone complete the same work?
Assumption:
Let's assume that the total work is represented by W.
Calculation:
Let's calculate the work done per day by P and Q together and by Q alone.
- Work done by P and Q together per day = W/8
- Work done by Q alone per day = W/12
Since P and Q together can complete the work in 8 days, the work done by P and Q together in 1 day is 1/8 of the total work.
Similarly, since Q alone can complete the work in 12 days, the work done by Q alone in 1 day is 1/12 of the total work.
From the given information, we can write the equation:
(W/8) + (W/12) = 1
To solve this equation, we need to find the common denominator:
(3W + 2W)/24 = 1
5W/24 = 1
Now, let's solve for W (total work):
5W = 24
W = 24/5
Therefore, the total work W is equal to 24/5.
Now, let's calculate the number of days it would take for P alone to complete the work.
- Work done by P alone per day = W/number of days taken by P alone to complete the work
Let's represent the number of days taken by P alone to complete the work as D.
So, the equation becomes:
(W/D) = 1
Substituting the value of W, we have:
(24/5)/D = 1
To solve for D:
24/5 = D
D = 24/5
Therefore, P alone can complete the work in 24/5 days.
Simplifying the fraction, we have:
D = 4.8
Since we cannot have a fraction of a day, we round up to the nearest whole number.
Hence, P alone can complete the same work in approximately 5 days.
Therefore, the correct answer is option A) 24.
P and Q together can complete a piece of work in 8 days.
Q alone can complete the same work in 12 days.
To find:
In how many days can P alone complete the same work?
Assumption:
Let's assume that the total work is represented by W.
Calculation:
Let's calculate the work done per day by P and Q together and by Q alone.
- Work done by P and Q together per day = W/8
- Work done by Q alone per day = W/12
Since P and Q together can complete the work in 8 days, the work done by P and Q together in 1 day is 1/8 of the total work.
Similarly, since Q alone can complete the work in 12 days, the work done by Q alone in 1 day is 1/12 of the total work.
From the given information, we can write the equation:
(W/8) + (W/12) = 1
To solve this equation, we need to find the common denominator:
(3W + 2W)/24 = 1
5W/24 = 1
Now, let's solve for W (total work):
5W = 24
W = 24/5
Therefore, the total work W is equal to 24/5.
Now, let's calculate the number of days it would take for P alone to complete the work.
- Work done by P alone per day = W/number of days taken by P alone to complete the work
Let's represent the number of days taken by P alone to complete the work as D.
So, the equation becomes:
(W/D) = 1
Substituting the value of W, we have:
(24/5)/D = 1
To solve for D:
24/5 = D
D = 24/5
Therefore, P alone can complete the work in 24/5 days.
Simplifying the fraction, we have:
D = 4.8
Since we cannot have a fraction of a day, we round up to the nearest whole number.
Hence, P alone can complete the same work in approximately 5 days.
Therefore, the correct answer is option A) 24.
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P and Q together can complete a piece of work in 8 days, Q alone can complete the same work in 12 days.In how many days can P alone complete the same work?a)24b)12c)18d)36Correct answer is option 'A'. Can you explain this answer?
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