Official Quant thread for CAT 2013

@veertamizhan said:
"In a stream running at 2 kmph, a man goes 10 km upstream and comes back to the starting point in 55 minutes. Find the speed of the boat in still water."
10 = (s-2)t1
10=(s+2)t2
just add then replace t1+t2 by 55/60
and find s
@jain4444 said:
_ S _ S _ S _ g1 + g2 + g3 + g4 = 2=> 5C3 * 4!/2! = 120when both c's are together g1 + g2 + g3 + g4 = 1 => 643 * 3! = 24 so , required answer = 120 - 24 = 96
when both C's are together, ke baad kaise aaya ?
@jain4444 said:
5 tanx = 18 , find value of (sinx - cox)
tanx =18/5 = p/b


=> h = rt(349)

sinx= p/h=18/h

cosx =b/h=5/h

so ans= 13/h
@jain4444 said:
5 tanx = 18 , find value of (sinx - cox)
easy one? Or some data is missing :neutral:

tan x=18/5
=> sin x=18/{sqrt(18^2+5^2}=18/_/349
cos x=5/_/349

==> sin x-cos x=13/_/349
@vijay_chandola said:
easy one? Or some data is missing tan x=18/5=> sin x=18/{sqrt(18^2+5^2}=18/_/349cos x=5/_/349==> sin x-cos x=13/_/349
or maybe some data is wrong
@veertamizhan said:
"In a stream running at 2 kmph, a man goes 10 km upstream and comes back to the starting point in 55 minutes. Find the speed of the boat in still water."
55/60=10/(v+2)+10/(v-2)

==> 11*v^2-44*v-240=0
or, v= 7.1
@jain4444 said:
5 tanx = 18 , find value of (sinx - cox)
13/rt349
@jain4444 said:
A and B together can do a piece of work in 16 days.B and C can do the same work in 32 days.After A worked for 4 days,B for 12 days,C takes up and finished it alone in 48 days.In how many days will each of them complete the work?
trying to solve the problem using some observations and very simple calculation (can be done almost mentaly)

A+B take half the time that of B+C

A works for 4 days. B for 12 and C for 48.

Since A and B complete in 16 days =>in 4days (A+B) finish (1/4) of job. { so 8 days of B and 48 days of C is left now}
Since B and C complete in 32 days =>in 8days (B+C) finish (1/4) of job { so 40 days of C is left now}

=>C completes the remaining (1/2) in 40 days => C finishes the work in 80 day

{Till this point it can be done verbally, from here on I have underlined the calculation steps for which we need pen and paper}

Now B+C finish in 32 days => C does 32/80 = 40% of work and B does 60% of work in 32 days

=>B can finish the work in 32/.6 = 160/3 days

A and B finish in 16 days
As found earlier B does 60% in 32 days => he does 30% in 16 days => A does 70% in 16 days. Hence A will take 16/.7 = 160/7 days.

Puys have already solved this question earlier and my answer is no different. What I have tried to do here is to break the conventional method and get a method which is faster and requires minimal pen and paper.

ATDH.
in mixing tea 1 % of tea is wasted. a
seller gain 10% by selling mixtur at
rs40/kg.find proportion in whixh he
shd mix two variety of tea costing rs
42 & 32
@jain4444 said:
in mixing tea 1 % of tea is wasted. aseller gain 10% by selling mixtur atrs40/kg.find proportion in whixh heshd mix two variety of tea costing rs42 & 32
let the cost of mixture be x
=> actual cost= 40/1.1*.99=40*.09=36

Now use allegations:
42________32
_____36_____
4__________6

==> mix the two varieties in 4:6 or 2:3 ratio
@jain4444 said:
in mixing tea 1 % of tea is wasted. aseller gain 10% by selling mixtur atrs40/kg.find proportion in whixh heshd mix two variety of tea costing rs42 & 32
42x+32y=40/1.1*(x+y)*99/100
42x+32y=36(x+y)
x/y=4/6=2/3??
@jain4444 said:
in mixing tea 1 % of tea is wasted. aseller gain 10% by selling mixtur atrs40/kg.find proportion in whixh heshd mix two variety of tea costing rs42 & 32
2:3

99/100*40/1.1=36 rs actual price

now apply allegation:

42 ____32
36
4 : 6

therefore ratio is 2:3
@jain4444 :

actual cost will be = 40/110 * 99 = 36 rs

so we need 36 by mixing 42& 32 so answer will be= 36-32: 42-36 = 4:6=2:3

@jain4444 2:3 :D`

@jain4444 said:
in mixing tea 1 % of tea is wasted. aseller gain 10% by selling mixtur atrs40/kg.find proportion in whixh heshd mix two variety of tea costing rs42 & 32
mine is lengthy way :(
.1={99*40-42x-(100-x)32}/{42x+(100-x)32}
x=40 and thus 100-x=60
Ratio=2/3 Not able to learn alligations yet some one teach me alligations
@ziddiarmaan said:
@jain4444 : actual cost will be = 40/110 * 99 = 36 rsso we need 36 by mixing 42& 32 so answer will be= 36-32: 42-36 = 4:6=2:3
bhai please explain first part of your solution...second part I understood :)
@TootaHuaDil : dekho he got 10% profit so .. 40is the 1.1 .. and 1% is wasted so 40/1.1 is 99% of x so

99% of x= 40/1.1 :)
A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current in kmph
@audiq7 said:
A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current in kmph
4kmph?

i knw easy hai par options mein kuchh gadbad lag rahi thi...


Deccan Queen travelling with 72kmph crosses a platform of length 100 meters in 20s. It crosses another tranin travelling in the same direction with 54kmph in 100s. Find the length of second train.