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In how many years would Bane be exactly thrice as old as his grandson?

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Math Expert
Joined: 02 Sep 2009
Posts: 54371
In how many years would Bane be exactly thrice as old as his grandson?  [#permalink]

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06 Aug 2017, 01:03
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Difficulty:

95% (hard)

Question Stats:

39% (03:20) correct 61% (02:29) wrong based on 39 sessions

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In how many years would Bane be exactly thrice as old as his grandson?

(1) In ten years, Bane would be 30 years more than twice his grandson’s age.
(2) Ten years back, Bane was 40 years more than thrice his grandson’s age.

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Re: In how many years would Bane be exactly thrice as old as his grandson?  [#permalink]

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06 Aug 2017, 02:03
It's a D.
Statement 1 . If we assume age of son as y then age of grandfather urns out to be 2y+40.

So we can solve and get the answer.
Statement 2: again if we assume age of son as y then that of father turns out to be 3y+20.

So this can also be solved for requisite answer.

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Re: In how many years would Bane be exactly thrice as old as his grandson?  [#permalink]

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06 Aug 2017, 02:07
In how many years would Bane be exactly thrice as old as his grandson?

Let, B be Bane's current Age and G his grandson't current age

Statement 1) In ten years, Bane would be 30 years more than twice his grandson’s age.

B+10 = 2(G + 10) + 30
B+10 = 2G + 20 + 30
B = 2G + 40

So if in n years, Bane will exactly thrice as old his grandson, then

B + n = 3 (G+n)
2G + 40 + n = 3G + 3n
G + 2n = 40

This statement is insufficient as we do not know the value of G.

Statement (2) Ten years back, Bane was 40 years more than thrice his grandson’s age.

B - 10 = 3 (G-10) + 40
B - 10 = 3G - 30 + 40
B = 3G + 20

This statement is not sufficient as we do not know the values of B and G

Combining both statements we get, B = 2G + 40 = 3G + 20 ==> G = 20

G + 2n = 40 ==> 20 + 2n = 40 ==> 2n = 20 ==> n = 10

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Re: In how many years would Bane be exactly thrice as old as his grandson?  [#permalink]

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06 Aug 2017, 03:44
Bunuel wrote:
In how many years would Bane be exactly thrice as old as his grandson?

(1) In ten years, Bane would be 30 years more than twice his grandson’s age.
(2) Ten years back, Bane was 40 years more than thrice his grandson’s age.

(1) B+10 = 30 + 2 (G+10)
B= 2G + 40

Not sufficient

(2) B-10 = 40 + 3(G-10)
B = 3G +20

Not Sufficient

On combining two equations two variables
Sufficient
D
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Re: In how many years would Bane be exactly thrice as old as his grandson?  [#permalink]

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06 Aug 2017, 06:15
1
let the age of bane and his son be x and y years respectively
and we need to find out: In how many years would Bane be exactly thrice as old as his grandson, let n be the required no. of years after which bane would be thrice as old as his grandson
so we have,
(x+n) = 3(y+n), by solving we get: n = (x-3y)/2 or we need the value of (x-3y).
Now lets look at the given statements
(1) In ten years, Bane would be 30 years more than twice his grandson’s age.
(x+10) = 2(y+10)+30, solving it, we get: x-2y=40, we reach nowhere with this, hence insuffificent

(2) Ten years back, Bane was 40 years more than thrice his grandson’s age.
(x-10) = 3(y-10)+40, solving it, we get: x-3y=20, and hence n=20/2=10
hence sufficient

hence B
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Re: In how many years would Bane be exactly thrice as old as his grandson?  [#permalink]

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06 Aug 2017, 06:22
1
Bunuel wrote:
In how many years would Bane be exactly thrice as old as his grandson?

(1) In ten years, Bane would be 30 years more than twice his grandson’s age.
(2) Ten years back, Bane was 40 years more than thrice his grandson’s age.

Bane -> B years
Gson-> G years
B+n = 3(G+n)
n = ?

1) B+10 = 2(G+10)+30
=> B = 2G+40
And B = 3G+2n
=> G = 40-2n
n=?
Insufficient.

2) B-10 = 3(G-10)+40
=> B = 3G + 20
and B = 3G + 2n
=> n = 10
Sufficient.

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Re: In how many years would Bane be exactly thrice as old as his grandson?   [#permalink] 06 Aug 2017, 06:22
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