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A typing work is done by three person P, Q and R. P alone takes 10 hours to type a single booklet but B and C working together takes 4 hours, for the completion of the same booklet. If all of them worked together and completed 14 booklets, then how many hours have they worked?
- a)30hrs
- b)40hrs
- c)25hrs
- d)45hrs
- e)50hrs
Correct answer is option 'B'. Can you explain this answer?
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A typing work is done by three person P, Q and R. P alone takes 10 hou...
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A typing work is done by three person P, Q and R. P alone takes 10 hou...
Given Information:
Three people, P, Q, and R, are involved in a typing work.
P takes 10 hours to type a single booklet.
Q and R together take 4 hours to complete a booklet.
Approach:
Let's assume that the total work to type a booklet is represented by "x".
We can find the individual work rates of P, Q, and R by using the concept of work done in unit time.
Calculations:
Let's assume the work done by P in 1 hour is "P's work rate".
Therefore, P's work rate = x/10
Similarly, let's assume the work done by Q in 1 hour is "Q's work rate" and the work done by R in 1 hour is "R's work rate".
Therefore, (Q's work rate) + (R's work rate) = x/4
Given that P, Q, and R together completed 14 booklets, we can equate the total work done by them with the work done by each person individually.
Total work done by P, Q, and R = (P's work rate + Q's work rate + R's work rate) × time taken
We need to find the total time taken by P, Q, and R together to complete the work.
Substituting the values, we have:
14x = [(x/10) + (x/4)] × time taken
Simplifying the equation, we get:
14 = (1/10 + 1/4) × time taken
Solving further:
14 = (2/20 + 5/20) × time taken
14 = (7/20) × time taken
Multiplying both sides by 20/7, we get:
time taken = 40 hours (option B)
Answer:
The three people worked together for 40 hours to complete the 14 booklets.
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