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  • IBPS SO CWE Exam Quantitative Aptitude Study Material

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Mixture and Allegations
A pipe can fill a tank in x hours and another can empty it in y hours. They can together fill it in (y > x )

a) X-y
b) Y-x
c) Xy/x-y
d) Xy/y-x



Answer
Solution
Correct Answer Is : Xy/y-x
Solution Is : Work done by A in one hour =1/x
work done by B in one hour=1/y
Both A and B together work in one hour=(1/x)-(1/y) =(y-x)/xy.
Both A and B fill tank in xy/(y-x) hours.
A tap can empty a tank in 30 minutes. A second tap can empty it in 45 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank ?

a) 18 minutes
b) 14 minutes
c) 15 minutes
d) 30 minutes



Answer
Solution
Correct Answer Is : 18 minutes
Solution Is : Work done by 1st tap in one minute =1/30
work done by 2nd tap in one minute =1/45
Both taps one minute work =(1/30)+(1/45)
=(45+30)/1350
=75/1350 =1/18.
Both tap will empty the tank in 18 minutes.
729 ml of a mixture contains milk and water in the ratio 7 : 2. How much more water is to be added to get a new mixture containing milk and water in the ratio 7 : 3 ?

a) 60 ml
b) 71 ml
c) 52 ml
d) 81 ml



Answer
Solution
Correct Answer Is : 81 ml
Solution Is : Quantity of milk =(7/9) *729 =567ml
Quantity of water =(2/9)*729 =162ml
Let `x` be the quantity that should be added to make the ratio 7:3.
According to the question, 567/(162+x) =7/3
=>1701 =1134+7x
=> 7x =1701 -1134
=>x=81ml
A shopkeeper bought 30 kg of rice at the rate of Rs. 70 per kg and 20 kg of rice at the rate of Rs. 70.75 per kg. If he mixed the two brands of rice and sold the mixture at Rs. 80.50 per kg, his gain is

a) Rs. 510
b) Rs. 525
c) Rs. 485
d) Rs. 450



Answer
Solution
Correct Answer Is : Rs. 510
Solution Is :
Pipe A can fill a tank in 4 hours and pipe B can fill it in 6 hours. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full ?

a) 4 1/2
b) 3 1/2
c) 3 1/4
d) 4 2/3



Answer
Solution
Correct Answer Is : 4 2/3
Solution Is : Part of tank filled in first two hours = 1/4 + 1/6 = (3+2)/12 = 5/12. Part of tank filled I first 4 hours =10/12 =5/6. Remaining part 1 - 5/6 =1/6. This remaining part will be filled by pipe A. Time taken by Pipe A = (1/6) *4 = 2/3 hour. Therefore total time = 4+(2/3) = 4 2/3
Two alloys contain tin and iron in the ratio of 1 : 2 and 2 : 3. If the two alloys are mixed in the proportion of 3 : 4 respectively (by weight), the ratio of tin and iron in the newly formed alloy is :

a) 10 : 21
b) 13 : 22
c) 14 : 25
d) 12 : 23



Answer
Solution
Correct Answer Is : 13 : 22
Solution Is : Let 3kg of first alloy and
4kg of second alloy could be mixed together.
Therefore, In 3kg of mixture,
Tin = 1kg
Iron = 2kg.
In 4kg of mixture,
Tin=(2/5)×4 = 8/5 kg=1.6kg
Iron=(3/5)×4=12/5=2.4kg
Therefore,Required ratio
=(1+1.6) : (2+2.4) =2.6 : 4.4
13 : 22
Two pipes A and B can fill a tank with water in 30 minutes and 45 minutes respectively. The water pipe C can empty the tank in 36 minutes. First A and B are opened. After 12 minutes C is opened. Total time (in minutes) in which the tank will be filled up is :

a) 30
b) 12
c) 36
d) 24



Answer
Solution
Correct Answer Is : 24
Solution Is : Part of tank filled by pipes A and B in 1 minute = (1/30)-(1/45)=1/18 part. Therefore,part of tank filled in 12 minutes=(12/15)=2/3 part Remaning part=1-(2/3)=1/3 part when pipe Cis opened,part of tank filled by all 3 pipes=(1/30)(1/45)-(1/36)=5/180=1/36. therefore,Time taken in filling 1/3 part = (1/3)*36=12 minutes, therefore,Total time=12+12 =24 minutes.
An empty pool being filled with water at a constant rate takes 8 hours to fill 3/5 th of its capacity. How much more time will it take to finish filling the pool ?

a) 4 hours 50 minutes
b) 5 hours 30 minutes
c) 5 hours 20 minutes
d) 4 hours 48 minutes



Answer
Solution
Correct Answer Is : 5 hours 20 minutes
Solution Is :
Pipe A is an inlet pipe filling the tank at 800 l/hr. Pipe B empties the tank in 3 hours. The capacity of the tank is

a) 12000 l
b) 8000 l
c) 6000 l
d) 4000 l



Answer
Solution
Correct Answer Is : 12000 l
Solution Is :
In what ration must 25% of alcohol be mixed with 50% of alcohol to get a mixture of 40% strent alcohol?

a) 1 : 2
b) 2 : 1
c) 2 : 3
d) 3 : 2



Answer
Solution
Correct Answer Is : 2 : 3
Solution Is : Given, 2. (r3) = 54 Þ r = 3
Two mean proportionals
= 2r & 2r2 = 2(3), 2(3)2
= 6, 18.
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