9. P and Q together finish a work in 30 days. They worked for 20 days and then Q left. The remaining work was done by P alone in 15 days. In how many days P alone can finish the total work?
Answers
Step-by-step explanation:
P + Q)'s 10 day's work= (1/30) x 10 = 1/3
Remaining work = (1 -1/3) = 2/3
2/3 work is done by P in 20 days.
∴ Whole work is done by P in 20 x (3/2) = 30 days
Step-by-step explanation:
Time taken by P to complete the work = 14 days
Time taken by Q to complete the work = 21 days
Q left work after = 6 days
Formula used:
If P and Q can do a piece of work in x and y days, respectively. They start working together and after t days Q leaves the work, then
Time taken to finish whole work = (x/y) × (y - t)
Calculation:
Here, P = 14 days, Q = 21 days, t = 6 days
According to the formula
Time taken to finish whole work = (x/y) × (y - t)
⇒ (14/21) × (21 - 6)
⇒ (2/3) × 15
⇒ 10 days
∴ The time taken to complete the work is 10 days.
Total work = 42 (L.C.M)
Efficiency of P = 3
Efficiency of Q = 2
P and Q work together for 6 days = 6 × (3 + 2)
Work completed = 30
Remaining work = 42 - 30
⇒ 12
Remaining work completed by P alone = 12/3
⇒ 4 days
Total time = 6 days + 4 days
⇒ 10 days
∴ The time taken to complete the work is 10 days.
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