Official Quant thread for CAT 2013

MBA CAT 2024
29989
@bodhi_vriksha said:
@heylady good .. Now try this one A circle C is such that it touches two sides of an equilateral triangle as well as the circumcircle of the given triangle. what is the ratio of areas of incircle :circle C: circumcircle.Team BV--Pratik Gauri
This question was posted yesterday. Please check pg 1517 or 1516....
29990
@bodhi_vriksha said:
@heylady good .. Now try this one A circle C is such that it touches two sides of an equilateral triangle as well as the circumcircle of the given triangle. what is the ratio of areas of incircle :circle C: circumcircle.Team BV--Pratik Gauri
cirucmcircle:circle:incircle=4:3:1?
29991
@iLoveTorres said:
4:3:1?
@bodhi_vriksha
I posted the answer as: 1: (2-sq rt 3)^2: 4
29992
@iLoveTorres said:
4:3:1?
@heylady said:
@bodhi_vrikshaI posted the answer as: 1: (2-sq rt 3)^2: 4
Approach.. both of you ..

Team BV--Pratik Gauri
29993
@catahead 20 hrs ..go by option
29994
@heylady said:
VOlume=1/3 * L^2 * HL=10 sqrt 3Lateral height^2= Height^2+ (Base)/(2)^2Lateral Height= Sqrt 75Now Surface area= Area of base+4 * area of triangular facesArea of base= area of square=300Area of triangular faces= 4* 1/2* sq root 300 * sq root 75Area of triangular faces= 300TSA= 300+300= 600
height = 10
base = 10_/3
lateral height = sqrt(175)
29995
@KhannaiiM said:
option c)
29996
@bodhi_vriksha said:
@heylady good .. Now try this one A circle C is such that it touches two sides of an equilateral triangle as well as the circumcircle of the given triangle. what is the ratio of areas of incircle :circle C: circumcircle.Team BV--Pratik Gauri
let the radius of circle c be r
Diameter of circumcircle = 2a/sqrt3 = let it be d
so (d-r)sin30 = r
r comes out to be = 2a/3sqrt3
ratio of radius = 1/2 : 2/3 : 1
ratio of areas = 9:16:36
29997
@raopradeep said:
two taps are running continously to fill a tank 1st one will take 5 hours by itself and 2nd one will 20 hours by itself. but operator failed to realise leak in the tank from beginning which caused a delay of 1 hour in filling tank find the time in which leak would empty a filled tank15202540
20 hrs.
29998
@raopradeep said:
two taps are running continously to fill a tank 1st one will take 5 hours by itself and 2nd one will 20 hours by itself. but operator failed to realise leak in the tank from beginning which caused a delay of 1 hour in filling tank find the time in which leak would empty a filled tank15202540
20 hrs ?

normal time -----> 1/5 + 1/20 = 5/20 = 4hrs
now because of a leak,there will be a delay of 1 hr

so 1/5 + 1/20 - 1/x = 1/5
x = 20 hrs
29999
@mailtoankit
30000
A yearly payment to a servant is Rs. 90 plus one turban. the servant leaves the job after 9 months and receives Rs. 65 and a turban. find the price of the turban..

a little confusion...plz post with approach...thanks
30001
@DivineSeeker said:
A yearly payment to a servant is Rs. 90 plus one turban. the servant leaves the job after 9 months and receives Rs. 65 and a turban. find the price of the turban..a little confusion...plz post with approach...thanks
10 Rs?
Suppose turban is of X Rs.
So his yearly payment was 90+X
So after 9 months he should get (90+X)*9/12
But instead he got 65+X.
So (90+X)*9/12 = 65+X
X= 10
30002
@adwaitjw u got it right....
30003
@amresh_maverick said:
There is a track on the outer boundary of a rectangular field ABCD (AB = 300m and BC = 200m). Initially Aman and Baman are at point A and B respectively. Both Aman and Baman start moving along the track in anti-clockwise manner at the same time with the same speed. If 'x' is the shortest possible distance between Aman and Baman at any instance then the minimum possible value of 'x' is (neglect the width of the track) a 150 m b 150√2 m c 200 m d 200√2 m e 300 m
Distance between them = 300 = (a+b) where a and b are perpendicular distances to each other.
Also, Shortest distance between them = _/(a^2 + b^2) = _/((a+b)^2 - 2ab)
= _/(300^2 - 2ab)

Minimise the shortest distance...
Maximise ab

a+b/2 >= _/ab

Maximum ab = 300^2/4

Shortest distance = _/(300^2/2) = 150_/2 ??
30004
@DivineSeeker said:
A yearly payment to a servant is Rs. 90 plus one turban. the servant leaves the job after 9 months and receives Rs. 65 and a turban. find the price of the turban..a little confusion...plz post with approach...thanks
For 12 months, salary = 90+T
So for 9 months shud be (90+T)*9/12 = 65+T
Solve and get T=10
30005
@psk.becks said:
let the radius of circle c be rDiameter of circumcircle = 2a/sqrt3 = let it be dso (d-r)sin30 = r r comes out to be = 2a/3sqrt3ratio of radius = 1/2 : 2/3 : 1ratio of areas = 9:16:36
bro yeh kaise aaya? mujhe toh kafi time laga to project and calculate the radius of the circle
30006
From a point P, the tangents PQ and PT are drawn to a circle with centre O and radius 2 units. From the centre O, OA and OB are drawn parallel to PQ and PT respectively. The length of the chord TQ is 2 units. Find the measure of the ∠AOB.

(a) 30° (b) 90° (c) 120° (d) 45°
30007
@albiesriram said:
From a point P, the tangents PQ and PT are drawn to a circle with centre O and radius 2 units. From the centre O, OA and OB are drawn parallel to PQ and PT respectively. The length of the chord TQ is 2 units. Find the measure of the ∠AOB.(a) 30° (b) 90° (c) 120° (d) 45°
120??
30008
A person can buy 20 sparrows for a rupee, a pigeon for a rupee, and a peacock for Rs. 5. Find the number of birds of each type he needs to buy if he wants to buy total 100 birds for Rs. 100 so that he buys at least one bird of each type.

ans is 19 peacock=95rs+80 sparrows=4 rs+ 1 pigeon=1 rs.

is there any mathematical approach for these kindaa questions if we pile up the data???