Official Quant thread for CAT 2013

@CSK23 said:
right. bhai why not x = 63 , 80 so on.. yesOA -8
Because it is mention in the question that we can take vaue of x from -50 to 50

@Amrofa said:
A shopkeeper marks up his goods by 40% and gives a discount of 10%. Apart from this, he uses a faulty balance also, which reads 1000gm for 800gm. What is the net profit percentage?
57.5%?

CP = 100 (for 1 kg)
for .8 kg , CP = 80

MP = 100*140/100 = 140
Discount = 10%-----SP = 140*90/100 = 126
net gain = 126 - 80/80*100 = 57.5%
@mailtoankit please provide the explanation.
@Amrofa said:
A shopkeeper marks up his goods by 40% and gives a discount of 10%. Apart from this, he uses a faulty balance also, which reads 1000gm for 800gm. What is the net profit percentage?
51.2%
@mailtoankit @saurav5517 : yup its 26.25. made a calculation error. please provide explanation.
@Amrofa said:
A shopkeeper marks up his goods by 40% and gives a discount of 10%. Apart from this, he uses a faulty balance also, which reads 1000gm for 800gm. What is the net profit percentage?
51.2%
@mailtoankit
@CSK23

Ans is 57.5 %
@Amrofa said:
A shopkeeper marks up his goods by 40% and gives a discount of 10%. Apart from this, he uses a faulty balance also, which reads 1000gm for 800gm. What is the net profit percentage?
let 1000grm cost 1000rupees..
he gives 800 instead of 1000
so his CP = 800...
now he marks up on 1000 by 40% -> 1400rs and then gives discount of 10%...hence his final sp = 1400 - 1400*10/100 = 1260..
hence, Profit% = (1260 - 800)/800 = 0.575 or 57.5 %
@Amrofa

Shld be 57.5%

Let 100 be the Original CP of 1000 gm of item..

Thus, MP= 140..Discount= 14...Final SP = 126..

Now, 800 gm of item is actually sold at 126..

Thus, 1000 gm of item is sold at 126/800*1000 = 157.5..

Thus, Profit% = (157.5 - 100)/(100)*100 = 57.5%..
@Amrofa yes

let intial price, 100 - 140 (40% increase) - 126 (10% discount)
800 -------- 126
200 -------- ? [ 1/4 (126) = 31.5 ] (profit)
total = 126+31.5 = 157.5
profit% = 57.5%

sory ppl m late..its 57.5%%%%.....

Q: In a base n, 32 * 45 = 2133. Express the number (424) of base 10 in base n.

ABCD is a trapezium with AD||BC. The diagonals of the trapezium intersect at O such that AO=3 , OC=x-3, DO= x-5, OB=3x-19 . Find the value of x.


a)8,9
b)7,8
c)8,10
d)7,10
e)none of these

PS: given answer- option a .
i got the answer e . one of the value of x is 8 but the other one wasn't 9. it was 13/3.
@saurav5517 said:
26.25 cms..??
bhai explanation?
@somnathbhatta said:
A triangle ABC with AB=17.5cm and AC=9cm is drawn. A perpendicular is dropped from A on BC at D with AD=3cm. Triangle ABC is circumscribed by a circle. Find the radius of the circumcircle. PS:- don't know the answer. please provide a less calculation intensive method.(i got an answer of 28.85cm)
explanation please

Eighty five children went to an amusement park where they could ride on the merry-go-round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re 1, and the total receipt of the amusement park was Rs 145.

How many children did not try any of the rides?


(1) 5 (2) 10 (3) 15 (4) 20

15. How many children took exactly one ride?

(1) 5 (2) 10 (3) 15 (4) 20

@CSK23

Shld be 1144..

Let n be the required base..

Thus, (32)n = 3n + 2...(45)n = 4n + 5...(2133)n = 2n^3 + n^2 + 3n + 3

Now, (3n + 2)*(4n + 5) = 2n^3 + n^2 + 3n + 3

=> 2n^3 - 11n^2 - 20n - 7 = 0

Thus, n=7..

Now, (424)10 = (1144)7..
@CSK23 i used heron's formula for circumcircle. a bit calculation intensive.

circumcircle = abc/4[{s(s-a)(s-b)(s-c)}^1/2]
@Amrofa said:
Eighty five children went to an amusement park where they could ride on the merry-go-round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re 1, and the total receipt of the amusement park was Rs 145.How many children did not try any of the rides?(1) 5 (2) 10 (3) 15 (4) 2015. How many children took exactly one ride?(1) 5 (2) 10 (3) 15 (4) 20
cost of children with 3 rides = 20x3=60rs, children with 2 rides= (55-20)x2=70rs,
children with 1 ride only=145-60-70=15
children with atleast 1 ride= 15+20+35= 70
children with no ride=80-70=10
@pyashraj said:
@CSK23Shld be 214..Let n be the required base..Thus, (32)n = 3n + 2...(45)n = 4n + 5...(2133)n = 2n^3 + n^2 + 3n + 3Now, (3n + 2)*(4n + 5) = 2n^3 + n^2 + 3n + 3=> 2n^3 - 11n^2 - 20n - 7 = 0Thus, n=7..Now, (424)n = 4*7^2 + 2*7 + 4 = 214..
(424) base 10 should be converted to base n i.e 7
OA: (1144) of base 7
@Amrofa said:
Eighty five children went to an amusement park where they could ride on the merry-go-round, roller coaster, and Ferris wheel. It was known that 20 of them took all three rides, and 55 of them took at least two of the three rides. Each ride cost Re 1, and the total receipt of the amusement park was Rs 145.How many children did not try any of the rides?(1) 5 (2) 10 (3) 15 (4) 2015. How many children took exactly one ride?(1) 5 (2) 10 (3) 15 (4) 20

15
5
lets see if I am right??