Official Quant thread for CAT 2013

MBA CAT 2024
12762
@pavimai

Let the rate of flow of 1 smaller pipe be x unit/hr..Thus, Rate of flow of 1 large pipe= 2unit/hr..Let V units be the Volm of the tank..n y unit/hr be the rate of leakage..

Now, Amt. of water filled when the tank was expected to be filled = V/(4*2x + 10x)*(18x - y)

Given,2/3*V = V*(18x-y)/18x

=> y =6x unit/hr..

Now, New rate of leakage = 3x unit/hr..

Given, V/18x = 15/2, or, V=135x Units..

Required Time, t = 1/3*V/(18x - 3x) = V/45x = 3hr..
12763

Q. Milk and water are mixed in a vessel A in the ratio 4:1 and in a vessel B in the ratio 5:2. Find,what quantities(in Kg.) should be taken from each of the vessels to have a new mixture consisting of 7 kg. of milk and 2 kg. of water.

12764
@pavimai said:
hypothetical question
No i asked coz if your score is more than mine then i have no right of advising you..:P
12765
@sails said:
No i asked coz if your score is more than mine then i have no right of advising you..
fundamental Right of Advicing Sanctioned
12766
@cadmium

Let x kg be taken from Vessel A..n Let y kg be taken from vessel B..

Thus, Total Miik = 4/5*x + 5/7*y , and, Total Water = 1/5*x + 2/7*y

Given, 4x/5 + 5y/7 = 7...(i) and , x/5 + 2y/7 = 2...(ii)

Solving (i) n (ii), we have, x(A) = 20/3 kg..and y(B) = 7/3 kg..
12767
@cadmium said:
Q. Milk and water are mixed in a vessel A in the ratio 4:1 and in a vessel B in the ratio 5:2. Find,what quantities(in Kg.) should be taken from each of the vessels to have a new mixture consisting of 7 kg. of milk and 2 kg. of water.

I am assuming the mixture is done based on weight and not volume.
vessel A=x kg
vessel B=y Kg

7=0.8x+(5/7)y
2=0.2x+(2/7)y

solving, x=6.66,y=2.33
12768
How many solutions will the following equation have:

a*b*c=40

where a,b,c are integers
12769
@bs0409 14??
@bs0409 said:
How many solutions will the following equation have:a*b*c=40where a,b,c are integers
12770
@pyashraj said:
, Total Miik = 4/5*x + 5/7*y , and, Total Water = 1/5*x + 2/7*y
I got it to some extent.
Can you please elaborate with some depth how to frame these equations?
12771
@bs0409 said:
I am assuming the mixture is done based on weight and not volume.vessel A=x kgvessel B=y Kg7=0.8x+(5/7)y2=0.2x+(2/7)ysolving, x=6.66,y=2.33
Sir,may I know how these equations are formed?
Please enlighten me with the rule of framing this equation.
Thanks.
12772
@sails 256 is ans
12773
@cadmium said:
Q. Milk and water are mixed in a vessel A in the ratio 4:1 and in a vessel B in the ratio 5:2. Find,what quantities(in Kg.) should be taken from each of the vessels to have a new mixture consisting of 7 kg. of milk and 2 kg. of water.
part of milk in A ==> 4/5 in B ==> 5/7 ..required part = 7/9

using alligation ratio in which A and B is to be mixed is (7/9 - 5/7 ) : ( 4/5 - 7/9) = 4/63 : 1/45 => 20:7
12774
@ravi.theja i solved in a very long approach .. using differentials .. is there any other method of solving it .. took me abt 10 mins to solve .. any better method ?

12775
@bs0409 said:
How many solutions will the following equation have:a*b*c=40where a,b,c are integers
18??
12776
@somnathbhatta said:
@ravi.theja i solved in a very long approach .. using differentials .. is there any other method of solving it .. took me abt 10 mins to solve .. any better method ?
Alligation method 😃 Refer any material u ll find it 😃 its nt possible xplaining it here :(
12777
@ravi.theja said:
18??
explain your method pls
12778

In what ratio should water be mixed with a liquid costing Rs.12 per litre,so as to make a profit of 25% by selling the diluted liquid at Rs.13.75 per litre?

12779
@bs0409 said:
How many solutions will the following equation have:a*b*c=40where a,b,c are integers
40 = 2^3*5


so we need to express this as product of 3 numbers - 4+2 = 6

30 ordered pairs

taking into account -ve integers = 30*4 = 120
12780
@bvdhananjay said:
explain your method pls
wrote down all possible combinations
(1,1,40 ) ===> 3 ways
(1,2,20) ===> 6 ways
(1,4,10 ) ===> 6 ways
(1,8,5) ===>6 ways
(2,2,10 ) ===> 3 ways
(2,4,5) ==> 6 ways
so total = 30 😃 shit..!!i missed sme cases earlier
12781
@cadmium said:
In what ratio should water be mixed with a liquid costing Rs.12 per litre,so as to make a profit of 25% by selling the diluted liquid at Rs.13.75 per litre?
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