Official Quant thread for CAT 2013

MBA CAT 2024
15903
@ani6 said:
Plz Help!!A tradesman fixes the sale price of his articles 30% more than the C.P.. Half of the articles , he sells at this increased sale price and portion , he sells at 15% discount of this sale price. And the remaining , he sells at 30% discount of this sale price . what % profit did occur to the tradesman?
question not clear.......ye to vahi baaat ho gayii aadhe idhar jao, aadhe udhar jao aur baake mere peeche...
15904

0.5*0.85*1.3*x +0.7*1.3*0.5 x =0.5*1.3x (1.55 )= 1.0075x


initial cost price was x, hence 0.75% increase in profit??
15905
@adityaknsit A tradesman fixed his selling price of goods at 30% above the cost price .He sells half the stock at this price,one quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price.find the the gain percent altogether.
15906
the value of ((1.001001001)^(1/3)) -((1.001001)^(1/3)) is closest to:

options: 0, 10^(-6), 3*10^(-9) , 3.3*10^(-10).
koi to batao bhaiya.
15907
@ani6 said:
@adityaknsit A tradesman fixed his selling price of goods at 30% above the cost price .He sells half the stock at this price,one quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price.find the the gain percent altogether.
29.625% profit?
15908
@Omkarp 15.375%

15909
@ani6 said:
@Omkarp 15.375%
Haan ab aaya mera 15.375%...I added the 30% discount. :splat:

Anyway, what was your approach?
15910
@ani6 said:
@adityaknsit A tradesman fixed his selling price of goods at 30% above the cost price .He sells half the stock at this price,one quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price.find the the gain percent altogether.
SP=1.3CP
Total SP= 50*1.3CP + 25 *0.85*1.3CP+25*.7*1.3CP
Sp=25*1.3CP(2+0.85+0.7)
=25*1.3CP(3.55)=115.375CP

TOTAL CP=100CP

Profit %=15.375%
15911
@ani6 said:
@adityaknsit A tradesman fixed his selling price of goods at 30% above the cost price .He sells half the stock at this price,one quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price.find the the gain percent altogether.
let there be 100 articles and let 100 be the CP of each of these 100 articles.

for half of the articles SP=130
for quarter of the articles Sp= 85/100*130=110.5
for remaining SP= 70*130/100=91
net profit= 30*50+ 10.5*25 - 9*25

=1500+ 262.5 - 225

= 1537.5

gain percent= 1537.5/100= 15.375%
15912
@anitito123 said:
the value of ((1.001001001)^(1/3)) -((1.001001)^(1/3)) is closest to:options: 0, 10^(-6), 3*10^(-9) , 3.3*10^(-10).koi to batao bhaiya.
bhai kuchh nahi pata chal raha...still thinking....
15913
@adityaknsit said:
let there be 100 articles and let 100 be the CP of each of these 100 articles.for half of the articles SP=130for quarter of the articles Sp= 85/100*130=110.5for remaining SP= 70*130/100=91net profit= 30*50+ 10.5*25 - 9*25=1500+ 262.5 - 225= 1537.5gain percent= 1537.5/100= 15.375%
Yea.. I did this only.. so much better without variables.
There isn't a better way, is there?
15914

Thanks all

15915
@Omkarp said:
Yea.. I did this only.. so much better without variables. There isn't a better way, is there?
well.....seemed better to me...there might have been a shorter way...but this didn't take much time either....I too am more comfortable with 100s than x,y or z's
15916
@anitito123 said:
the value of ((1.001001001)^(1/3)) -((1.001001)^(1/3)) is closest to:options: 0, 10^(-6), 3*10^(-9) , 3.3*10^(-10)Plz mention the approach.

ans= 3.3*10^(-10)

I used the binomial expansion of (1 + x)^n

(1 + x)^n =1+ nx + n(n − 1)./2! x^2 + n(n − 1)(n − 2)/3! x^3


now

(1.001001001)^(1/3))= (1 +.001001001)^1/3= 1 +1/3*(.001001001)........ignoring higher order terms......

(1.001001)^(1/3)=(1 +.001001001)^1/3= 1 +1/3*(.001001001)


subtracting them


1/3(.001001001-.001001001)

= 1/3(10^(-9))

ans ---3.3*10^(-10)
15917
@anitito123 said:
the value of ((1.001001001)^(1/3)) -((1.001001)^(1/3)) is closest to:options: 0, 10^(-6), 3*10^(-9) , 3.3*10^(-10).koi to batao bhaiya.
0?
3.3x10 ^(-10)
use binomial expansion for fractional index - (1 + x) ^n = 1 + nx + ....
15918
@adityaknsit @techgeek2050 correct!!thanks both for reiterating the formula for binomial expansion with fractional index!!
15919
@pyashraj maximum value of k= 103. just check the power of lowest prime number that is 2
15920

A sector with acute angle theta is cut from a circle of dia 12m.The radius of the circle circumscribed about the sector is?

options: 3cos(theta/2),3sec(theta/2), 3cos theta, 3 sec theta


15921
@anitito123
Is the answer 3Sec(theta/2)?

The situation is analogous to a situation where we find the circumradius for a triangle! Formula for circumradius is abc/4A (a,b,c are sides of the triangle and A is its area) From some trigonometric deductions (Jay baba class 10) we get the answer as above!
15922
@anitito123 said:
A sector with acute angle theta is cut from a circle of dia 12m.The radius of the circle circumscribed about the sector is?options: 3cos(theta/2),3sec(theta/2), 3cos theta, 3 sec theta
3sec(theta/2)
using formula a/san A=2R
where R--> radius of circumscribed circle