Ratios Problem

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neoshichhadva: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Wed May 25, 2011 10:51 pm

by neoshichhadva » Mon Sep 19, 2011 9:38 am

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

[spoiler]Answer: C[/spoiler]

Can someone please explain how to solve?

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Source: Beat The GMAT — Problem Solving | Mon Sep 19, 2011 9:38 am

Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Mon Sep 19, 2011 9:47 am

neoshichhadva wrote: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

[spoiler]Answer: C[/spoiler]

Can someone please explain how to solve?

Let the Initial number of stamps of Kaye and Alberto be 5a and 3a , ratio of stamps with Kaye & Alberto is 5a /3a

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

So , 5a - 10 /3a + 10 = 7/5

25a - 50 = 21a + 70

4a = 120

So , a = 30

So initially Kaye gave Alberto had , 150 and 90 stamps....

Later , Kaye gave Alberto 10 of her stamps

So stamps with Kaye and Alberto after giving 10 stamps is :

Kaye : 140

Alberto : 100

So difference between them is 140 -100 = 40 stamps...

Option C.

Abhishek

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Mon Sep 19, 2011 9:49 am

5x and 3x initially.
5x-10 / 3x+10 = 7/5
25x-50 = 21x + 70
x=30
thus final: 140 and 100
140-100=40
IMO C

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Cans!!

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Sep 19, 2011 9:51 am

Kalye/Alberto = 5X/3X

After, Kayle gives Alberto 10 of her stamps,

ratio becomes - 5X-10/(3X+10) = 7/5 (New ratio given)

Solve for X; we get X=30.

Therefore; Stamps Kayle has = 5X-10 = 140
Alberto = 3X+10 = 100

Difference = 40

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