Official Quant thread for CAT 2013

@vbhvgupta said:
A person calculate his % profit on cp and another on SP.what will be their diff in profit if both claims a profit of 20% on goods sold for rs 3000.
Profit for case 1: 500 (20% on CP)
Profit for case 2 : 600 (20% on SP)

Hence difference = 100 ?

@scrabbler Sir good morning :)
Aap bhi bhai waali tone mein aa gaye ..mast :D
@vbhvgupta said:
explain?
case 1 : x + x/5 = 3000 CP = 2500 Profit =500
case 2 : (3000-x)/3000 = 1/5 CP = 3000 Profit = 600
so diff 100..hope i understood the problem correctly...
@scrabbler said:
Up to 20 she is allowed, need not be exactly 20.Bhai dekh na....the question is asking how many sweets did she buy....if she is buying 20 sweets exactly then the question is a waste?regardsscrabbler
yeah you can take any number of sweets, the bottomline is the shop costs 3 rs more and her uncle's shop costs her 3rs less.. jus had a look at your solution. Aapke solution mein she is spending 3rs more at her uncle's shop

P.S While typing the previous msg i thought finally i have been able to make @scrabbler agree to my solution :(

@rachit_28 said:
Profit for case 1: 500 (20% on CP)Profit for case 2 : 600 (20% on SP)Hence difference = 100 ?@scrabbler Sir good morning Aap bhi bhai waali tone mein aa gaye ..mast
Main to humesha hi aisa tha! Good morning :)

regards
scrabbler

@rnishant231
@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..

cn u plz xplain ur approach???
@vbhvgupta said:
A person calculate his % profit on cp and another on SP.what will be their diff in profit if both claims a profit of 20% on goods sold for rs 3000.
Bhai general way mai profit cp pe nikalta hai....is case mai dono pe nikalna hai...
case 1:profit on cp
sp-cp/cp =20/100 cp comes out to be 2500 profit p1=500
Case 2:profit on sp
sp-cp/sp=20/100 cp comes out to be 2400 profit p2=600
hence p1-p2=100
A train aftr travelling 50 km frm A meets with an accident and proceeds at 4/5th of the former speed and reaches B,45 min late.had the accident happened 20 km further on ,it would hav arrived 12 min sooner.find the original speed & the distance
@iLoveTorres said:
A train aftr travelling 50 km frm A meets with an accident and proceeds at 4/5th of the former speed and reaches B,45 min late.had the accident happened 20 km further on ,it would hav arrived 12 min sooner.find the original speed & the distance
25 and 125?

regards
scrabbler

@simplydevesh said:
@rnishant231@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) 280No of Ways = 120 + 96 + 72 + 48 + 24 = 360..cn u plz xplain ur approach???
1 _ _ _ _ _ _ 120 ways
A 1 _ _ _ _ _ A can be any thing other than 1 and 6 and then arrange the others in 4! : 4*4!
A B 1 _ _ _ 4C2 * 2! *3!= 72
A B C 1 _ _ 4C3 * 3! * 2!= 48
A B C D 1 6 : 4!=24

ttal=360
@simplydevesh said:
@rnishant231@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) 280No of Ways = 120 + 96 + 72 + 48 + 24 = 360..cn u plz xplain ur approach???
Taking 1 in the first place - no. of possiblity = 5! =120
For 2nd position - 4.4.3.2.1 = 96..
For 3rd Position - 4.3.3.2.1 = 72
and so on..

However a better approach was posted by @Exodia

No. of ways to place 1 and 6= 6c2
No. of arrangements of the rest of the numbers= 4!
Answer= 6c2. 4!
=360

@scrabbler said:
25 and 125?regardsscrabbler
bro what is the mistake in my approach,
see the breakdown in the first case occurs at 50kms and in the second case it occurs at 70kms
So in first case the distance 50-70 is travelled at 4s/5 and in the second case it is travelled at normal speed s.
The time taken in the two cases constitutes to the time difference which is 33 mins
hence
20/(4s/5) - 20/s = 33/60
i am getting s=100/11 :(
@rnishant231 said:
Taking 1 in the first place - no. of possiblity = 5! =120 For 2nd position - 4.4.3.2.1 = 96..For 3rd Position - 4.3.3.2.1 = 72and so on..However a better approach was posted by @ExodiaNo. of ways to place 1 and 6= 6c2 No. of arrangements of the rest of the numbers= 4! Answer= 6c2. 4! =360
Even less effort required if we realise that either 1 comes before 6 or 6 before 1. By symmetry neither is more likely - and hence exactly half of the 6! i.e 720 ways should have 1 before 6. Hence 360.

regards
scrabbler

@scrabbler said:
Even less effort required if we realise that either 1 comes before 6 or 6 before 1. By symmetry neither is more likely - and hence exactly half of the 6! i.e 720 ways should have 1 before 6. Hence 360.regardsscrabbler
yessssssss i realised after doing all the hard work... is pe confidence nahi tha...
@iLoveTorres said:
bro what is the mistake in my approach,see the breakdown in the first case occurs at 50kms and in the second case it occurs at 70kmsSo in first case the distance 50-70 is travelled at 4s/5 and in the second case it is travelled at normal speed s.The time taken in the two cases constitutes to the time difference which is 33 minshence20/(4s/5) - 20/s = 33/60i am getting s=100/11
The time difference between the two cases has to be seen, which is 12 min. I quote:

...had the accident happened 20 km further on ,it would hav arrived 12 min sooner...

regards
scrabbler

@scrabbler said:
Even less effort required if we realise that either 1 comes before 6 or 6 before 1. By symmetry neither is more likely - and hence exactly half of the 6! i.e 720 ways should have 1 before 6. Hence 360.regardsscrabbler

Thanks sir...dimaag ki batti haule haule jalne lagegi...
@scrabbler bhai zara yeh bhi orally solve kardo

Two trains A & B start frm stations X & y towards each other.B leaves station Y half an hour aftr train A leaves station X.two hrs aftr train A has strtd,the dist between the trains A & B is 19/30th of the dist between stations X & y.how much time would it take each train (A & B) to cover the distance X to Y,if train A reaches half an hr ltr to its dest as compared to B.
@iLoveTorres said:
@scrabbler bhai zara yeh bhi orally solve kardoTwo trains A & B start frm stations X & y towards each other.B leaves station Y half an hour aftr train A leaves station X.two hrs aftr train A has strtd,the dist between the trains A & B is 19/30th of the dist between stations X & y.how much time would it take each train (A & B) to cover the distance X to Y,if train A reaches half an hr ltr to its dest as compared to B.
So, let's look at what we know.

A starts 0.5 hours before and finishes 0.5 hours fter. So the times taken are 1 hour apart.

Abhi tak 2 hours ho gaya for A and 1.5 and total distance is just over 1/3, which means total time should be around 6 times (1.5 to 2) which is 9-12 ke range mein

Denominator 30 hai, so I want two consecutive numbers which will lend themselves to 30...is it too much of a stretch to take 9 and 10?

So if B takes 9 hours and A 10, let us check - assume 90 ka distance, so B going 10 per hour, A going 9, and in 2 hours A will have done 18 and in 1.5 hours B will have done 15 so total is 33/90 = 11/30 leaving 19/30.

Hence 9 hrs and 10 hrs is fine. (Yes, did it orally. Painful though)

regards
scrabbler

@iLoveTorres said:
A train aftr travelling 50 km frm A meets with an accident and proceeds at 4/5th of the former speed and reaches B,45 min late.had the accident happened 20 km further on ,it would hav arrived 12 min sooner.find the original speed & the distance
speed will be 25
distance 125
50/v + d-50/0.8v= t+3/4
70/v + d-70/0.8v = t+11/20
d=tv
solving it v=25
d=125
@iLoveTorres said:
@scrabbler bhai zara yeh bhi orally solve kardoTwo trains A & B start frm stations X & y towards each other.B leaves station Y half an hour aftr train A leaves station X.two hrs aftr train A has strtd,the dist between the trains A & B is 19/30th of the dist between stations X & y.how much time would it take each train (A & B) to cover the distance X to Y,if train A reaches half an hr ltr to its dest as compared to B.
time of a =10 time of b =9
@simplydevesh said:
@rnishant231@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) 280No of Ways = 120 + 96 + 72 + 48 + 24 = 360..cn u plz xplain ur approach???
simplest approach
_ 1___ 6_
now these 3 marks have to be filled by 4 numbers
a+b+c=4 --solutions 6c2
but these 4 numbers can also be arranged in 4! ways so
6c2*4!=360