Two pipes A and Y can fill a cistern in 24 min. and 32 min

Two pipes A and Y can fill a cistern in 24 min. and 32 min. respectively. If both the pipes are opened together, then after how time Y should be closed so that the tank is full in 18 minutes?
(a) 6 min
(b) 8 min
(c) 10 min
(d) 12 min

Anurag Mishra Professor Asked on 13th March 2016 in Maths.
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    Answer: (b) 8 min 

    Solution:-
    Let B be closed after X min.
    then ,  part filled by (A+B) in X min. + part filled by  A in (18-X)min.=1
    Therefore,  X x ((1/24)+(1/32))+(18-x) x (1/24)=1   6 (7 X/96) + ((18-X)/24)=1.
    ó7 X +4 x (18-X)=96.

    Hence, be must be closed after 8 min.

    Anurag Mishra Professor Answered on 14th March 2016.
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