Official Quant thread for CAT 2013

@Cat.Aspirant123 said:
A trader has bought some goods at a discount of 20% on the list price. He wants to mark them atsuch a price that even if he gives a discount of 20% on the marked price he still makes a profit of25%. If he marks the goods by 20% points more than the proposed price and allows a discount of50%, then what will be the profit / loss percentage?(1) 27.5% profit (2) 30% loss (3) 27.5% loss (4) 30% profit (5) None of these
List price =100
CP=80
MP*.8=80*1.25
MP=125
SP=100

MP=150
SP=75
Loss=5
5/80*100
5*5/4=6.25%
A cyclic quadrilateral of maximum area is drawn inside a circle and is painted blue. Find the percentage of area not painted.
A container contains 40 litres of solution of milk and water with milk and water in the ratio of 2:3.4 litres of water is added and then 4 litres of mixture is taken out.This process is repeated once more.Find the milk to water ratio now.?

From: http://www.pagalguy.com/prep/quantitative/time-speed-distance-wo-t-84470/q-3617013
@Cat.Aspirant123 said:
A cyclic quadrilateral of maximum area is drawn inside a circle and is painted blue. Find the percentage of area not painted.
36.3%
@krum said:
36.3%
ya steps
@Cat.Aspirant123 said:
A cyclic quadrilateral of maximum area is drawn inside a circle and is painted blue. Find the percentage of area not painted.
= (area of circle - area of square) : ( area of circle)
since radius = side * (_/2/2)
on solving you'll get = 4 * (1/11) * 100 ~ 36%
@sowmyanarayanan said:
36% ?
ya app
@Cat.Aspirant123 said:
A cyclic quadrilateral of maximum area is drawn inside a circle and is painted blue. Find the percentage of area not painted.
Cyclic Quad= Square
let side of square be a and radius of circle be r
acc to the question,
a= r_/(2)

Required area percentage= (pi*r^2- a^2)*100/pi*r^2
=> (22/7-2)*100/22/7= 36 (approx)
@sowmyanarayanan said:
A container contains 40 litres of solution of milk and water with milk and water in the ratio of 2:3.4 litres of water is added and then 4 litres of mixture is taken out.This process is repeated once more.Find the milk to water ratio now.?From:www.pagalguy.com/prep/quantita...



40:81

@nramachandran said:
40:81
sir approach please..
@sowmyanarayanan said:
= (area of circle - area of square) : ( area of circle) since radius = side * (_/2/2)on solving you'll get = 4 * (1/11) * 100 ~ 36%
@maddy2807 said:
Cyclic Quad= Squarelet side of square be a and radius of circle be racc to the question,a= r_/(2)Required area percentage= (pi*r^2- a^2)*100/pi*r^2=> (22/7-2)*100/22/7= 36 (approx)
Is there any way to prove that square will be of maximum area??
@sowmyanarayanan said:
A container contains 40 litres of solution of milk and water with milk and water in the ratio of 2:3.4 litres of water is added and then 4 litres of mixture is taken out.This process is repeated once more.Find the milk to water ratio now.?From:www.pagalguy.com/prep/quantita...
M- 400/27 , W - 680/27

after 4 liters of water is added - M - 400/27 , W - 788/27

after 4 liters of solution is removed - M - 400/27-4*(400/27*44) = 400/27-400/27*11
M = 4000/27*11
W - 788/27-788/27*11 = 7880/27*11

after 4 liters of water is added again - M - 4000/27*11 , W - 9068/27*11

after replacement - M - 4000/27*11-4*4000/27*11*11 = 40000/27*11*11
W - 90680/27*11*11

so M:W - 4000:9068 - 1000:2267
@sowmyanarayanan said:
A container contains 40 litres of solution of milk and water with milk and water in the ratio of 2:3.4 litres of water is added and then 4 litres of mixture is taken out.This process is repeated once more.Find the milk to water ratio now.?From:www.pagalguy.com/prep/quantita...
quantity of milk=16{1-(4/44)}^2=1600/121
quantity of water=40-1600/121=3240/121
hence ratio =40:81
@htomar said:
Is there any way to prove that square will be of maximum area??
An n sided cyclic polygon will have largest area when it is a regular polygon
@sowmyanarayanan said:
A container contains 40 litres of solution of milk and water with milk and water in the ratio of 2:3.4 litres of water is added and then 4 litres of mixture is taken out.This process is repeated once more.Find the milk to water ratio now.?From:www.pagalguy.com/prep/quantita...
ans is 40:81

There might be other approaches for this question, I was comfortable with this one.
Since we added water to the solution, quantity of milk remain constant while adding water,
Initially, milk=16 lt
water=24 lt

ratio of milk after adding 4 lts of water into it= 16/44= 4/11
After removal of 4 lts solution, quantity of milk in the solution is,
=> 16- 4*4/11= 160/11

Now again adding 4 lts of water to it make the ratio of milk in the solution= 160/(11*44)=40/121

after removal of 4 lts of solution, quantity of milk remains= 160/11-40*4/121= 1600/121

since we had 40 lts of solution, remaining must be water, hence
=>40-1600/121= 3240/121

req ratio= 1600:3240= 40:81
80% milk solution is mixed with 30% milk solution to produce 45 liter of 50% milk solution. If the price of 45 liter of 50% milk solution is Rs. 1,080 and the price of 30% milk solution is Rs. 20 per liter, then what is the price of 80% milk solution in the final mixture?
@Cat.Aspirant123 said:
80% milk solution is mixed with 30% milk solution to produce 45 liter of 50% milk solution. If the price of 45 liter of 50% milk solution is Rs. 1,080 and the price of 30% milk solution is Rs. 20 per liter, then what is the price of 80% milk solution in the final mixture?
.8x+.3(45-x)=45*.5

==> x=18

so 18 liters of 80% sol. is mixed with 27 liters of 30% sol

1080 - 20*27 = 540
In the middle of a circular park of radius 2r units, a circular hole of radius r units has been dug. The mud extracted from the hole has been spread uniformly over one third of the rest of the park, to make an elevated platform around the hole. This has led to an increase of 5 units in initial depth of the hole. Find the percentage increase in depth of the hole.
@Cat.Aspirant123 said:
In the middle of a circular park of radius 2r units, a circular hole of radius r units has been dug. The mud extracted from the hole has been spread uniformly over one third of the rest of the park, to make an elevated platform around the hole. This has led to an increase of 5 units in initial depth of the hole. Find the percentage increase in depth of the hole.
[4*pi*r^2 - pi*r^2] /3* 5 = pi*r^2*h

==> h = 5

so 100% increase
@bullseyes said:
A rope is cut into 3 pieces of unequal lengths. Find the length of shortest piece.1) Length of 2 longest pieces is 12 cm2) Length of 2 shorter pieces is 11 cm. a) can be answered by a aloneb) can be answered by b alonec) can be answered by using bothd) can be answered by eithere) cannot be answered
cannot be answered?