PIPES AND CISTERNS SHORTCUTS FOR QUANTITATIVE APTITUDE
The above concept of 100% could be applied to the questions related to pipes and cisterns. We will do one question and you will understand the link between questions related to time and work & pipes and cisterns.
_______________________________________Q.1. Tap A can fill the tank in 8 hours and another hole B can empty the tank in 16 hours.If both are opened simultaneously in how many hours the tank will be full?
solution: Tap A can do the work of filling the tank in 8 hours. So work done in 1 hour= 100%/8= 12.5%
Hole B can do the work of emptying the tank in 16 hours. So work done in 1 hour= 100%/16 = 6.25%
If both A and B work simultaneously, % of the tank filled(work done) in 1 hour= 12.5 - 6.25 = 6.25%.
So time in which the 100% of the work will be done=100%/6.25=16 hours.
In this way we can asociate each and every questions related to time and work to questions related to pipes and cisterns and solve the questions.
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RULE OF FRACTION
Q. 15 men can do a work in 20 days. in how many days will 20 men do the full work?
solution:first case:
M1= 15 D1= 20
second case:
M2=20 D2= ?
here there are two variables. men and days. we have full information about men but we have to find the number of days in the second case.
we have to see what is the effect of increase or decrease in no.of men on the no.of days in second case. we see the no. of men has increased in the second case as compared to the first case. so we can easily use our common sense that when no. of men will increase the no. of days required to complete the task will decrease as each day more work will be done. so, to find the answer we have to do the following calculations,
D2=20x( 15/20){as there is decreasing effect on the no. of days we will
multiply D1 with lower fraction of M1 and M2(i.e.15/20).if
there had been increasing effect we would have multiplied
D1 with higher fraction of M1 and M2(i.e. 20/15)}
answer=15 days.
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Q.a garrison of 2200 men has provision for 16 weeks at the rate of 45 gms per day per men. how many men must leave so that the same provision may last for 24 weeks at 33 gm per day per man?
solution: first case:
m1=2200 w1=16 p1 =45
second case:
m2=? w2=24 p2=33
here we have to see the effect of increase or decrease in other variables on m2 :
weeks has increased so if weeks increases less men will be supported.
provision has decreased so more men will be supported.
m2=2200 . 16/24 . 45/33=2000
so we see with given variables in the second case only 2000 men will be supported. so (2200-2000) =200 men should leave.
Q.if 15 books cost Rs 35, what do 21 books cost?
ans. b1=15 c1=35
b2=21 c2=?
so, c2= 35x(21/15)=Rs 49.00
in this way we can see this rule of fraction is applicable to any area whereever there is comparision.
