%

[rahul.s]

Wing Yee has two types of stamps in her stamp collection: foreign stamps and domestic stamps. After she makes a purchase at a collectors' show, the number of stamps in Wing Yee's collection increases by 5 percent. If the number of foreign stamps in her collection increases by 4 percent and the number of domestic stamps in her collection increases by 8 percent, what percent of the stamps in her collection before the purchase were domestic?

A) 20 %
B) 25 %
C) 33 %
D) 50 %
E) 75 %

OA: B

[fibbonnaci]

Here are my notations:
T= total number of stamps
D= number of domestic stamps
F= number of foreign stamps
Tn = new stamps total
Fn= new foreign stamps
Dn= new domestic stamps.

According to the question:
F+D = T ---- (1)

Tn= (105/100)T

Fn= (104/100) F

Dn= (108/100) D

(105/100) T = (104/100) F + (108/100) D

ie. 104 F + 108 D = 105 T ----- (2)

combining both the equations and solving them simultaneously,
you get D= T/4

the questions asks you to determine the percentage of D in the total number of stamps.
ie. D/T = ?

T/4T => 1/4 => 25%

Hence B is the answer.

[ajith]

Wing Yee has two types of stamps in her stamp collection: foreign stamps and domestic stamps. After she makes a purchase at a collectors' show, the number of stamps in Wing Yee's collection increases by 5 percent. If the number of foreign stamps in her collection increases by 4 percent and the number of domestic stamps in her collection increases by 8 percent, what percent of the stamps in her collection before the purchase were domestic?

A) 20 %
B) 25 %
C) 33 %
D) 50 %
E) 75 %

OA: B

say F - No of foreign stamps D - No of domestic stamps

F(1.04) + D (1.08) = (F+D) (1.05)

0.04 F + 0.08 D = F+D (0.05)

0.04 F/D +0.08 = (F/D +1) ).05

0.01 F/D = 0.03

F/D = 3

% Domestic stamps = D/ D+F *100= 1/(1+F/D)*100 = 25%

[thephoenix]

Wing Yee has two types of stamps in her stamp collection: foreign stamps and domestic stamps. After she makes a purchase at a collectors' show, the number of stamps in Wing Yee's collection increases by 5 percent. If the number of foreign stamps in her collection increases by 4 percent and the number of domestic stamps in her collection increases by 8 percent, what percent of the stamps in her collection before the purchase were domestic?

A) 20 %
B) 25 %
C) 33 %
D) 50 %
E) 75 %

OA: B

let forign stamp=Fs

domestic stamps=Ds

total=t
we are asked to find Ds/t

Fs+Ds=t---->Fs=t-Ds

t2=1.05t
Fs2=1.04 Fs
Ds2=1.08Ds
Fs2+Ds2=t2
--->1.04Fs+1.08Ds=1.05t
insert Fs=t-Ds
1.04t-1.04Ds+1.08Ds=1.05t
or 0.04Ds=0.01t
orDs/t=1/4=25%

[rahul.s]

wow! amazing explanations. thank you

[sanju09]

Wing Yee has two types of stamps in her stamp collection: foreign stamps and domestic stamps. After she makes a purchase at a collectors' show, the number of stamps in Wing Yee's collection increases by 5 percent. If the number of foreign stamps in her collection increases by 4 percent and the number of domestic stamps in her collection increases by 8 percent, what percent of the stamps in her collection before the purchase were domestic?

A) 20 %
B) 25 %
C) 33 %
D) 50 %
E) 75 %

OA: B

If x out of a total of 100 of the stamps in her collection before the purchase were domestic, then (100 - x) of the stamps in her collection were foreign at then. When 5 more stamps were purchased, which were, let's say, d domestic, and 5 - d foreign, then

x + d = 1.08 x and 100 - x + 5 - d = 1.04 (100 - x)

or d = 0.08 x = 1 + 0.04 x

or 0.04 x = 1 or x = [spoiler]25%[/spoiler].

[spoiler]B[/spoiler]

[sumanr84]

Really amazed to see different approaches for this simple problem..
Nice work guys !! Human brain is really complex..everyone has got a diff way of attacking a Q..wow!!