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A pipe can fill a tank in 7 hours. Another pipe can empty the filled tank in 9 hours. If both the pipes are opened simultaneously, then the time
Question

A pipe can fill a tank in 7 hours. Another pipe can empty the filled tank in 9 hours. If both the pipes are opened simultaneously, then the time (in hours) in which the tank will be two-third filled, is:

A.

63

B.

21

C.

42

D.

84

Correct option is B

Given:

Pipe A fills the tank in 7 hours

Pipe B empties the tank in 9 hours 

Required work = 23\frac 23​ of the tank.

Solution:

work rate = 17\frac 17​ per hour.

work rate = -19\frac 19​ per hour.

Net rate when both are open = 1719\frac17 – \frac19​​
Net rate =(97)63=263 \frac {(9 – 7) }{ 63} =\frac 2{63}​ per hour
Time =23263\frac{\frac 23}{\frac2{63}}​  = 21 hours

Alternate Method:

Time taken to fill the tank = ​6397=632\frac{63}{9-7}=\frac{63}2​​

Required work = 23\frac 23​ of the tank = 23×632=\frac 23 \times \frac{63}2 = 21 hours​

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