Question 20

Three pipes P, Q and R can fill a tank in 10, 15 and 20 hours separately. P was opened at 7 AM, Q at 8 AM and R at 9 AM. At what time was the tank completely filled if R can work for only 3 hours at a stretch and needs a 1 hour break?

Solution

P was opened at 7 AM, Q at 8 AM and R at 9 AM

At 12 Pm

P run for 5 h, Q run at 4h, R run at 3h

$$p=6\times5=30$$

$$Q=4\times4=16$$

$$R=3\times3=9$$

Total fill at 12 am=30+16+9=55

Remaning =60-55=5

R at break after 3 hour ,only P & Q open for half and hour

total efficiency of P and Q=6+4=10

tank filled by P & Q in half and hour

$$=10\times\frac{1}{2}=5$$

So tank totally filled at 12:00 +00:30

$$=12:30 PM$$

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