Official Quant thread for CAT 2013

@ScareCrow28 said:
A mixture of milk and water in the ratio of 8:7. Another mixture of milk and water in the ratio of 5:9. In what ratio should we mix these two, if you need a mixture of milk and water in the ratio of 1:1?Copied from CGL Thread
30:7 ?
@ScareCrow28 said:
A mixture of milk and water in the ratio of 8:7. Another mixture of milk and water in the ratio of 5:9. In what ratio should we mix these two, if you need a mixture of milk and water in the ratio of 1:1?Copied from CGL Thread
30/7...
@Narci said:
NOT?
Is this same as choosing 150 balls from among 4 boxes containing 50,50,50 and 100 balls each ?

P.S : currently struggling with PnC
@Exodia said:
A dice is rolled six times. One, two, three, four, five and six appears on consecutive throws of dices. How many ways are possible of having 1 before 6?1) 1202) 3603) 2404) 280
OA: 360
No. of ways to place 1 and 6= 6c2
No. of arrangements of the rest of the numbers= 4!
Answer= 6c2. 4!
=300
@RDN said:
1:4
OA: 30:7

@Buck.up said:
30:7 ?
That's right.
@Narci said:
30/7...
Tell me where am I wrong ( Must be fundamentally wrong somewhere :banghead: )

Mix-1: Milk = 8ml, Water = 7 ml
Mix-2: Milk = 5ml, Water = 9ml

Ratio: k:1

8k + 5 / (5k + 9) = 1

from here, k = 4

Hence ratio = 4:1
You can also check it by putting the value of "k"
Please tell me where am I going wrong.

@abhishek.2011 Tum b dekho bhai..
@albiesriram said:
(50-a)+(50-b)(50-c)+(100-d)= 150,a+b+c+d = 100 = > 103c 3 none of the above?
Nyce explanation
@Exodia said:
Nyce explanation
it carried one glitch now changed. please take a look at it.
@ScareCrow28 said:
A mixture of milk and water in the ratio of 8:7. Another mixture of milk and water in the ratio of 5:9. In what ratio should we mix these two, if you need a mixture of milk and water in the ratio of 1:1?Copied from CGL Thread
30 : 7 ?

how can we approach this orally ?
@Exodia said:
OA: 360No. of ways to place 1 and 6= 6c2No. of arrangements of the rest of the numbers= 4!Answer= 6c2. 4! =300
in exactly half of the arrangements 1 will precede 6 .We can conclude there since total arrangements are 720.
@rnishant231 said:
30 : 7 ?how can we approach this orally ?
That only @scrabbler can tell! :)
@ScareCrow28 said:
A mixture of milk and water in the ratio of 8:7. Another mixture of milk and water in the ratio of 5:9. In what ratio should we mix these two, if you need a mixture of milk and water in the ratio of 1:1?Copied from CGL Thread
it will be 30:7
8/15x + 5/14 = x/2 + 1/2
x = 30/7
@Narci how 30/7? can u pls explain briefly, it seems scarecrow and i have misunderstood the qsn..
@ScareCrow28
Bhai I did using Alligation.
Most fundamental rule in Alligation is that it could only and only be applied on a single quantity at a time. Either take milk or water but not both.

Milk in 1st mix=8:15
Milk in 2nd mix=5:14
Milk in final mix=1:2

8/15.........5/14
........1/2
1/7...........1/30

Ratio 1/7 : 1/30 =30:7

Will get same answer if we take only water.

Here I think you are taking both quantities at same time that's why you got a wrong answer though fundamentally this approach looks right.
@Exodia said:
A dice is rolled six times. One, two, three, four, five and six appears on consecutive throws of dices. How many ways are possible of having 1 before 6?1) 1202) 3603) 2404) 280
No of Ways = 120 + 96 + 72 + 48 + 24 = 360..
@Buck.up said:
@ScareCrow28Bhai I did using Alligation.Most fundamental rule in Alligation is that it could only and only be applied on a single quantity at a time. Either take milk or water but not both.Milk in 1st mix=8:15Milk in 2nd mix=5:14Milk in final mix=1:28/15.........5/14........1/21/7...........1/30Ratio 1/7 : 1/30 =30:7Will get same answer if we take only water.Here I think you are taking both quantities at same time that's why you got a wrong answer though fundamentally this approach looks right.
If you look at the question first then it seems wrong, but what if we look at the answer first?
We can see that it , eventually, is satisfying the problem, isn't it? :rolleyes:
I still don't know where and how am I wrong. @scrabbler Please help on this.
@albiesriram said:
(50-a)+(50-b)+(50-c)+(100-d)= 150,a+b+c+d = 100 = > 103c 3 none of the above?The answer is not yet over this will contain values such as (51,x,y,z)= invalid. we have to exclude those cases.so consider when(51+a)+b+c+d= 100 or a+b+c+d = 49 or 52 c3 cases for a so in total , 3 * 52 C3 cases we have to exclude. a and b or c cannot be simultaneously greAter than 50. and d alone cannot be greater than 100. so no other exclusions. Hence OA should be 103C3 - 3*52C3
yup i was about to write all this thanks u save me from so much typing :)

it will be 103c3 - 3*52c3
it is because in 103c3 we will have all the cases when a or b or c is greater than 50 which is unfavourable
so we have to subtract them
answer will be 110551 :)
@ScareCrow28 said:
OA: 30:7 That's right. Tell me where am I wrong ( Must be fundamentally wrong somewhere )Mix-1: Milk = 8ml, Water = 7 mlMix-2: Milk = 5ml, Water = 9mlRatio: k:18k + 5 / (5k + 9) = 1from here, k = 4Hence ratio = 4:1You can also check it by putting the value of "k" Please tell me where am I going wrong.
i do in the way like...

taking LCM of both solutions...

that is solution 1 = 15l.. and solution 2 = 14l..

so LCM = 210

now,

mix 1 : Milk = 112l, water = 98l

mix 2 : Milk = 75l, water = 135 l...

let ratio be k:1

now... 112k + 75 / 98k + 135 = 1:1
112k + 75 = 98k + 135

14k = 60
k = 30/7...
@ScareCrow28 i got our mistake...total quantities of mixture are in the ratio 60:14 = 30:7 in our case also
basically, original volumes are in the ratio 15:14, we multiplied by 4:1, hence final answer is 30:7
basic error...
@ScareCrow28 said:
A mixture of milk and water in the ratio of 8:7. Another mixture of milk and water in the ratio of 5:9. In what ratio should we mix these two, if you need a mixture of milk and water in the ratio of 1:1?Copied from CGL Thread
@rnishant231 said:
30 : 7 ?how can we approach this orally ?
@ScareCrow28 said:http://lickthestranger.files.wordpress.com/2012/07/challenge-accepted.png
That only @scrabbler can tell!


http://lickthestranger.files.wordpress.com/2012/07/challenge-accepted.png

First one is divided into 8 + 7 = 15 parts, second in 5 + 9 = 14 parts. So take 210 (LCM of 14 and 15) parts. Now milk in first solution is 14 x 8 = 112, second is 15 x 5 = 75 and we need 1:1 i.e. 105 out of 210 parts milk. So see the difference of 112 and 75 from 105 - they are 7 and 30 so reverse this and voila, 30:7 is the ratio required.

regards
scrabbler

@scrabbler said:
First one is divided into 8 + 7 = 15 parts, second in 5 + 9 = 14 parts. So take 210 (LCM of 14 and 15) parts. Now milk in first solution is 14 x 8 = 112, second is 15 x 5 = 75 and we need 1:1 i.e. 105 out of 210 parts milk. So see the difference of 112 and 75 from 105 - they are 7 and 30 so reverse this and voila, 30:7 is the ratio required. regardsscrabbler
same method deployed by me...