1000+ Bank of America Aptitude Test Questions and Answers - 1
Question: 1
A pipe can fill a tank in x hours and another pipe can empty it in y (y > x) hours. If both the pipes are open, in how many hours will the tank be filled?
(A) (x - y) hours
(B) (y - x) hours
(C) $${xy}/{x - y}$$ hours
(D) $${xy}/{y - x}$$ hours
Ans: D
Net part filled in 1 hour = $$({1/x} - {1/y})$$ = $$({y-x}/{xy})$$
∴ The tank will be filled in $$({xy}/{y-x})$$hours.
Question: 2
Two pipes A and B can fill a tank in 15 hours and 20 hours respectively while a third pipe C can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed. In how much time will the tank be full?
(A) 10 hrs
(B) 12 hrs
(C) 14 hrs
(D) 16 hrs
Ans: B
Part filled in 10 hours = 10$$({1/15} +{1/20} - {1/25})$$ = $${23}/{30}$$
Remaining part = $$(1 - {23}/{30})$$ = $${7}/{30}$$
(A + B)’s 1 hour’s work = $$({1/15} + {1/20})$$ = $${7}/{60}$$: $${7/60} : {7/30}$$: : 1 : x
or x = $$({7/30} × 1 × {60/7})$$ = 2 hours.
∴ The tank will be full in (10 + 2) hrs = 12 hrs.
Question: 3
Pipe A can fill a tank in 10 hours. Pipe B can fill the same tank in 15 hours. Pipe C can empty the full tank in 20 hours. Pipes A, B and C are opened alternatively for one hour each. If A is opened first, then how many hours will they take to fill the empty tank?
(A) $$24{2}/{3}$$ hrs
(B) 24 hrs
(C) 25 hrs
(D) 27 hrs
Ans: A
(A + B + C)’s 3 hours work when opened alternately
= $$({1/10} + {1/15} - {1/20})$$ = $${7}/{20}$$
Part filled in (3 × 8) i.e. 24 hrs = $$({7}/{60} × 8)$$ = $${14}/{15}$$.
Remaining part = $$(1 - {14}/{15})$$ = $${1}/{15}$$
Now it is A’s turn $${1}/{10}$$ part is filled by A in 1 hr.
$${1}/{15}$$ part will be filled by A in $$(10 × {1}/{15})$$ hrs = $${2}/{3}$$ hr.
So, total time taken = $$24{2}/{3}$$ hrs.
Question: 4
A bath can be filled by the cold water pipe in 10 minutes and by the hot water pipe in 15 minutes. A person leaves the bathroom after turning on both the pipes. He returns just when the bath should have been full. Finding however, the waste pipe was open, he closes it. In 4 minutes more, the bath is full. In what time will the waste water pipe empty it?
(A) 6 minutes
(B) 8 minutes
(C) 9 minutes
(D) 10 minutes
Ans: C
Part filled by two inlet pipes in 1 min = $${1/10} + {1/15}$$ = $${1}/{6}$$.
Part filled by two inlet pipes in 4 min = $$(4 × {1}/{6})$$ = $${2}/{3}$$.
Time after which the waste pipe is closed
= Time taken by two inlets to fill the bath = 6 min.
Part filled by (2 inlets + 1 waste pipe) in 6 min
= $$(1 - {2}/{3})$$ = $${1}/{3}$$.
Part filled by (2 inlets + 1 waste pipe) in 1 min
= $$({1/3} × {1/6})$$ = $${1}/{18}$$.
∴ Work done by waste pipe in 1 min
= $$({1/18} - {1/6})$$ = -$${1}/{9}$$. [- ve sign means emptying].
Question: 5
Two pipes can fill a tank in 12 hours and 16 hours respectively. A third pipe can empty the tank in 30 hours. If all the three pipes are opened and function simultaneously, they in how much time the tank will be full?
(A) $$8{8}/{9}$$hours
(B) $$9{1}/{2}$$hours
(C) $$10{4}/{9}$$hours
(D) $$11{2}/{4}$$hours
Ans: A
First pipe fill the tank in 1 hour = $${1}/{12}$$ part of tank
Second pipe fill the tank in 1 hour = $${1}/{16}$$ part of tank
Third pipe empty the tank in 1 hour = $${1}/{30}$$ part of tank
When all three pipes are opened simultaneously, part of the tank filled in 1 hour.
= $${1/12} + {1/16} - {1/30}$$
LCM of 12, 16 and 30 = 240
= $${20 + 15 - 8} / {240}$$ =$${27}/ {240}$$
∴ Required time taken by all the three pipes = $${240}/{27}$$ = $${80}/{9}$$ = $$8{8}/{9}$$hours.
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