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# If James is currently 1/3 as old as his mother, how old is James?

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Math Expert
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If James is currently 1/3 as old as his mother, how old is James?  [#permalink]

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28 Aug 2017, 02:36
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15% (low)

Question Stats:

83% (01:30) correct 17% (01:27) wrong based on 114 sessions

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If James is currently 1/3 as old as his mother, how old is James?

(1) In 10 years, James will be half as old as his mother will be then.
(2) James is now twice as old as he was 5 years ago.

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Re: If James is currently 1/3 as old as his mother, how old is James?  [#permalink]

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28 Aug 2017, 02:37
Bunuel wrote:
If James is currently 1/3 as old as his mother, how old is James?

(1) In 10 years, James will be half as old as his mother will be then.
(2) James is now twice as old as he was 5 years ago.

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Re: If James is currently 1/3 as old as his mother, how old is James?  [#permalink]

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28 Aug 2017, 02:49
LET JAMES BE J YEARS OLD AND HIS MOTHER IS M
3J=M

1) (J+10)= 0.5(M+10) AND ALSO 3J=M, GIVES J=10 AND M=30
2) J= 2(J-5) , GIVES J=10 AND WE KNOW M=3J =30
THEREFORE BOTH ARE SUFFICIENT

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If James is currently 1/3 as old as his mother, how old is James?  [#permalink]

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28 Aug 2017, 02:54
1
Bunuel wrote:
If James is currently 1/3 as old as his mother, how old is James?

(1) In 10 years, James will be half as old as his mother will be then.
(2) James is now twice as old as he was 5 years ago.

Statement 1
- $$\frac{(J+10)}{(3J+10)} = \frac{1}{2}$$ --> $$2J+20 = 3J+10$$ --> $$-J=-10$$, thus J=10 years old.
- SUFFICIENT

Statement 2
- $$(J-5)*2 = J$$ --> $$2J-10=J$$, thus J=10 years old
- SUFFICIENT

D.
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If James is currently 1/3 as old as his mother, how old is James?  [#permalink]

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12 Oct 2017, 09:46
Hi,
Solution follows:

James is currently 1/3 as old as his mother => J=M/3 => M=3J

Statement 1: In 10 years, James will be half as old as his mother will be then => J+10 = M+10/2 (substitute M=3J) on solving we get J=10 (Sufficient)

Statement 2: James is now twice as old as he was 5 years ago => J=2(J-5) => J=10 (Sufficient)

Hope this helps
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Re: If James is currently 1/3 as old as his mother, how old is James?  [#permalink]

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27 Nov 2017, 19:17
Bunuel wrote:
If James is currently 1/3 as old as his mother, how old is James?

(1) In 10 years, James will be half as old as his mother will be then.
(2) James is now twice as old as he was 5 years ago.

We can let James’ current age = j and James’ mother's current age = m.

We have the following equation:

j = (1/3)m

3j = m

Statement One Alone:

In 10 years, James will be half as old as his mother will be then.

In 10 years, James will be (j + 10) and his mother will be (m + 10). The relationship between those two ages is that James will be ½ his mother’s age. We can create the following equation:

j + 10 = (m + 10)(1/2)

2j + 20 = m + 10

2j + 10 = m

Since 3j = m:

2j + 10 = 3j

j = 10

Statement one is sufficient to answer the question.

Statement Two Alone:

James is now twice as old as he was 5 years ago.

We can create the following equation:

j = 2(j - 5)

j = 2j - 10

j = 10

Statement two is sufficient to answer the question.

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Re: If James is currently 1/3 as old as his mother, how old is James? &nbs [#permalink] 27 Nov 2017, 19:17
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