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# Each of A and B has a few marbles with them. If A gives 12

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Manager
Joined: 18 Jul 2019
Posts: 54
Each of A and B has a few marbles with them. If A gives 12  [#permalink]

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25 Nov 2019, 07:30
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Difficulty:

35% (medium)

Question Stats:

62% (01:59) correct 38% (02:25) wrong based on 21 sessions

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Each of A and B has a few marbles with them. If A gives 12 marbles to B, the ratio of the number of marbles with them becomes the reciprocal of the initial ratio. If they together have a total of N marbles, how many marbles should A give to B so that each of them has an equal number of marbles?

a) 6
b) 12
c) 24
d) 26
e) 30
Math Expert
Joined: 02 Aug 2009
Posts: 8292
Re: Each of A and B has a few marbles with them. If A gives 12  [#permalink]

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26 Nov 2019, 18:19
CaptainLevi wrote:
Each of A and B has a few marbles with them. If A gives 12 marbles to B, the ratio of the number of marbles with them becomes the reciprocal of the initial ratio. If they together have a total of N marbles, how many marbles should A give to B so that each of them has an equal number of marbles?

a) 6
b) 12
c) 24
d) 26
e) 30

Let the number be A:B..
After A gives 12 marbles to B, the ratio becomes = B:A = A-12:B+12

$$A(A-12)=B(B+12).......A^2-12A=B^2+12B......A^2-B^2=12(B+A)....(A-B)(A+B)=12(A+B).....A-B=12$$
So A has 12 more marbles than B.

If A gives 6 to B, both will have equal number of marbles..

A
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Re: Each of A and B has a few marbles with them. If A gives 12   [#permalink] 26 Nov 2019, 18:19
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