Official Quant thread for CAT 2013

@Brooklyn said:
a company manufactures a car by spending some .this car is sold to to the showroom at 20% profit.this showroom sells it to ramu,a customer by making 15% profit.after a year,ramu sells the car to a second hand dealer at 30% loss who in turn sells it to another customer shamu at 5% profit margin for rupees 1,01,430.how much does the company spend for manufacturing the car?
100000.

Let the original price be x, then x *6/5 * 23/20 * 7/10 *21/20 = 101430. So x * 20286/20000 = 101430 which gives x as 100000.

regards
scrabbler

============================================
Ramesh wanted to invest an amount for a week. He also wanted to guarantee maximum returns on his investment. He was considering 3 alternatives for the investment. He can utilize each of these completely or partially along with the others. The alternatives are given below.
Alternative 1:
Invest in the mutual fund of X limited.if a rise occurs in the stock market hewould get 8% return.if a fall occurs in it,he would get -5% return.
Alternative 2:
Invest in the mutual funds of Y limited.if a rise occur in the stock market,he would get -4% return.if a fall occurs in it,he would get 3%return.
Alternative 3:
Invest in a bank which assures 0.15% return.

============================================
Q1. Find the greatest assured return to Ramesh?
a. 0.2%
b. 0.15%
c. 0.25%
d. 0.3%
=============================================
Q2. Find the strategy which will maximize the assured return to Ramesh.
a. Equal investment in each alternative
b. 35% in alternative 1 and 65% in alternative 2
c. 40% in alternative 1 and 60% in alternative 2
d. 60% in alternative 1 and 40% in alternative 2
=============================================
PS: Don't have OA. Quote your solution with only Ramesh. :)
@Torque024 said:
============================================Ramesh wanted to invest an amount for a week. He also wanted to guarantee maximum returns on his investment. He was considering 3 alternatives for the investment. He can utilize each of these completely or partially along with the others. The alternatives are given below.Alternative 1:Invest in the mutual fund of X limited.if a rise occurs in the stock market hewould get 8% return.if a fall occurs in it,he would get -5% return.Alternative 2:Invest in the mutual funds of Y limited.if a rise occur in the stock market,he would get -4% return.if a fall occurs in it,he would get 3%return.Alternative 3:Invest in a bank which assures 0.15% return.============================================Q1. Find the greatest assured return to Ramesh?a. 0.2%b. 0.15%c. 0.25%d. 0.3%=============================================Q2. Find the strategy which will maximize the assured return to Ramesh.a. Equal investment in each alternativeb. 35% in alternative 1 and 65% in alternative 2c. 40% in alternative 1 and 60% in alternative 2d. 60% in alternative 1 and 40% in alternative 2=============================================PS: Don't have OA. Quote your solution with only Ramesh.
0.2% by investing 35:65....I guess this is a CAT 07 question? Solved by a geometry approach...am not able to draw it on current comp 😞

regards
scrabbler

@Torque024 said:
============================================Ramesh wanted to invest an amount for a week.he also wanted to guarantee maximum returns on his investment.he was considering 3 alternatives for the investment.he can utilize each of these completely or partially along with the others .the alternatives are given below.Alternative 1:Invest in the mutual fund of X limited.if a rise occurs in the stock market hewould get 8% return.if a fall occurs in it,he would get -5% return.Alternative 2:Invest in the mutual funds of Y limited.if a rise occur in the stock market,he would get -4% return.if a fall occurs in it,he would get 3%return.Alternative 3:Invest in a bank which assures 0.15% return.============================================Q1. find the greatest assured return to ramesh?a. 0.2%b. 0.15%c. 0.25%d. 0.3%=============================================Q2. find the strategy which will maximize the assured return to ramesh.a. equal investment in each alternativeb. 35% in alternative 1 and 65% in alternative 2c. 40% in alternative 1 and 60% in alternative 2d. 60% in alternative 1 and 40% in alternative 2=============================================PS: Don't have OA. Quote your solution with only ramesh.


Q1. a
Q2. b

Consider investment of 100Rs. Out of which x is in Investment scheme 1.. And Remaining in 2.
If anything has to be invested in third scheme also then Combined returns of both the schemes should be less than .15%. We will Check all the cases now.

Consider profit case...
(x*108/100)+(100-x)*96/100 = 96+ (12*x/100)

Consider Loss case
(x*95/100) + (100-x)*103/100 = 103 - (8*x/100)

Now put options answers of second question here...
U will get max return in case of option b i.e. 35% in scheme 1 and 65% in scheme 2. And it comes out to be 0.20% .

As it is greater than 0.15%, our assumption of not investing in scheme 3 is correct.
And hence the answer for 1st Q is 0.20%

@Brooklyn said:
a company manufactures a car by spending some .this car is sold to to the showroom at 20% profit.this showroom sells it to ramu,a customer by making 15% profit.after a year,ramu sells the car to a second hand dealer at 30% loss who in turn sells it to another customer shamu at 5% profit margin for rupees 1,01,430.how much does the company spend for manufacturing the car?
1,00,000
Find area of square if 2x -3y + 7 = 0 and 6x - 9y + 8 = 0 represent 2 sides of square
@bullseyes said:
Find area of square if 2x -3y + 7 = 0 and 6x - 9y + 8 = 0 represent 2 sides of square
13/9
@deedeedudu said:
13/9
logic??
@Brooklyn said:
logic??
Distance between parallels = root(13)/3 = side of square
@Brooklyn said:
logic??
Distance between parallel lines
[7/root(13)]-[8/3root13]=root13/3=side of the square
@bullseyes said:
Find area of square if 2x -3y + 7 = 0 and 6x - 9y + 8 = 0 represent 2 sides of square
Distance between these two parallel lines= |7-8|/(sqrt(2^2+3^2)=1/sqrt(13)

=> Area =1/13
@vijay_chandola said:
Distance between these two parallel lines= |7-8|/(sqrt(2^2+3^2)=1/sqrt(13)=> Area =1/13
8/3 hoga na
@deedeedudu said:
Distance between parallel lines[7/root(13)]-[8/3root13]=root13/3=side of the square
how did u calculate distance b/w d lines??
@bullseyes said:
Find area of square if 2x -3y + 7 = 0 and 6x - 9y + 8 = 0 represent 2 sides of square
both r parallel lines
so distance between them = side of square=root13/3
area=13/9
@Brooklyn said:
how did u calculate distance b/w d lines??
Distance between any point (x1,y1) and a line of the form ax+by+c=0 is
|ax1+by1+c|/root(a^2+b^2)
Find the length from origin and subtract
@Brooklyn said:
how did u calculate distance b/w d lines??

Co-Geo formula. Distance between parallel lines ax + by + c1 and ax + by + c2 is given by |c2-c1|/rt(a^2+b^2)

regards
scrabbler

@vijay_chandola said:
Distance between these two parallel lines= |7-8|/(sqrt(2^2+3^2)=1/sqrt(13)=> Area =1/13
ur application is correct.. only think is that coefficients of both equation shld be equal.
If S1 denotes sum of squares of sides of trapezium and S2 denotes sum of squares of diagonals, S1-S2 = 576 and length of longer parallel side is 50 cm then find length of shorter parallel side.
@bullseyes said:
ur application is correct.. only think is that coefficients of both equation shld be equal.
did correctly in rough :O

Silly mistake

yeah it should be |7-8/3|/{sqrt(2^2+3^2)}
@bullseyes said:
If S1 denotes sum of squares of sides of trapezium and S2 denotes sum of squares of diagonals, S1-S2 = 576 and length of longer parallel side is 50 cm then find length of shorter parallel side.
Is 26 the ans? :embarrassed: