Problem Solving

The number of stamps that Kaye and Alberto had were in the ratio 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

A) 20
B) 30
C) 40
D) 60
E) 90

Thanks!

The number of stamps that Kaye and Alberto had were in the ratio 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

C) 40

K:A = 5:3 => K = 5x and A = 3x

After Kaye gave Alberto 10 of her stamps

K: A = 5x-10 : 3x+10 = 7:5

5x-10/3x+10 = 7/5

5(5x-10) = 7(3x+10)

25x-50 = 21x+70 => x = 30

K = 5x-10 = 5(30)-10 = 140
A = 3x+10 = 3(30)+10 = 100

K-A = 140-100 = 40

Kaye and Alberto ratio is 5:3

when we say ans is C i.e. 40

then Kaye and Albert can be 100:60 i.e. 5:3 right?

now, after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5

the number of stamps should be 90:70 which is not 7:5

but if we take D i.e. 60

then say Kaye and Albert is 150:90 (i.e. 5:3)
now if Kaye gives 10 stamps to Alberto then its 140:100 which is 7:5

I'm making some stupid mistake... but wot is it?

any comments?
Thanks!

I am on the same line .. but i doubt its 40 !!

Will be happy if i am proved wrong

Vishu

K:A = 5:3 => ket kaye have K stamps and Alberto A stamps

K/A= 5/3

or 3K=5A


After Kaye gave Alberto 10 of stamps

Kaye has k-10 and alberto A+10

5K-10/3A+10 = 7/5

5(5K-10) = 7(3K+10)

5k-7A=120

we know that K=5/3A

25A-21A=360
A=90 and K =150

Therefore K-A = 150-90 = 60

Answer should be 40, because the last sentence of the question says, as a result of this what is the difference. 140/100 = 7/5

Difference = 40.

Can we have the official answer please?

My answer is C

Sorry I understood the problem and corrected the solution:


K:A = 5:3 => let kaye have K stamps and Alberto A stamps

K/A= 5/3

or 3K=5A


After Kaye gave Alberto 10 of stamps

Kaye has k-10 and alberto A+10

5K-10/3A+10 = 7/5

5(5K-10) = 7(3K+10)

5k-7A=120

we know that K=5/3A

25A-21A=360
A=90 and K =150

after the stamp exchange:

A has 100
and K has 150-10=140

difference = 40

K-A=40

mehravikas wrote:Answer should be 40, because the last sentence of the question says, as a result of this what is the difference. 140/100 = 7/5

Difference = 40.

Can we have the official answer please?

OA: 40

The ratio of stamps of Kaye and Alberto is 5:3.
Then the total stamps Kaye has = 5x and the total stamps Alberto has is 3x.

Now,Kaye gives 10 stamps to Alberto.
It means Kaye has 5x-10 stamps and Alberto has 3x + 10 stamps. That is in the ratio 7:5.Cal x.Cal 5x-10 , cal 3x+10.Subtract.We get 40.

Not a standard method, but this is the way i solved..

via the multiples of LCM of the ratio's..

eg 1st ratio is 5:3 (so 8 is the base 5+3)
2nd ratio is : 7:5 (12 is base)

LCM of 8 and 12 is 24

24, 48, 72, 96, 120, 240 etc..

hit and try using 120
1st ratio is 75:45
2nd 70:50
this could be correct if "5" was decreased. So for 10, try it using 240
150: 90
140:100 --> ans(difference is 40)
bingo !!

its hard to explain in paper, but logically it would be easy to think.

Suyog wrote:Kaye and Alberto ratio is 5:3

when we say ans is C i.e. 40

then Kaye and Albert can be 100:60 i.e. 5:3 right?

now, after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5

the number of stamps should be 90:70 which is not 7:5

but if we take D i.e. 60

then say Kaye and Albert is 150:90 (i.e. 5:3)
now if Kaye gives 10 stamps to Alberto then its 140:100 which is 7:5




I'm making some stupid mistake... but wot is it?

Basic funda is that, if u multiply any no. or ratio with some num then , u have to do the reverse operation on it as well.

It is 40.

Original ratio = 5:3

Kaye - 150 Alberto- 90 (5:3)

After giving 10 stamps

Kaye - 140 Alberto- 100 (7:5)

I solved in the same manner as done by pre-gmat
Please help!!
x/y = 5/3
Then why are we taking

5x-10/3y+10= 7/5
Shouldn't it be

x-10/y+10= 7/5