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"You were a quarter of my age when I was twice of your present age"

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"You were a quarter of my age when I was twice of your present age"  [#permalink]

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New post Updated on: 11 Jan 2017, 09:26
5
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

58% (02:36) correct 42% (03:05) wrong based on 55 sessions

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"You were a quarter of my age when I was twice of your present age", said A to B. "5 years from now, our ages will add up to 45. How old was I, when you were born?"

A.10
B.15
C.20
D.25
E.22

Originally posted by 0akshay0 on 11 Jan 2017, 09:23.
Last edited by Bunuel on 11 Jan 2017, 09:26, edited 1 time in total.
Renamed the topic.
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New post 11 Jan 2017, 09:27
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New post 11 Jan 2017, 09:30
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New post 11 Jan 2017, 10:19
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Top Contributor
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Hi 0akshay0,

While solving age problems such as these there are three things that will help you solve such questions quickly and without any tedious working.

1. Limit the number of variables you choose to solve the question (Choose one or at most 2 variables)
2. Always put in the data given in age problems in a table with past, present and future ages as the rows and the people (A, B and C) as columns
3. Always read the question in parts and translate the statements into mathematical equations

Let the present age of 'B' be 'x'. "You were a quarter of my age when I was twice of your present age", said A to B.
So in the past A's age was 2x and B's age in the past was x/2. Let these past ages be 'y' years ago.

Attachment:
Capture.PNG
Capture.PNG [ 3.22 KiB | Viewed 2305 times ]


The present age of 'A' will now be '2x + y' and the present age of 'B' which is 'x' will be 'x/2 + y'. So y = x/2.

"5 years from now, our ages will add up to 45" ------> 2x + y + 5 + x + 5 = 45 ------> 2x + x/2 + 5 + x + 5 = 45. Simplifying we get

3x + x/2 = 35 -----> x = 10. So B's present age is 10. 5 years ago B's age was 5 and A's age was 20. So when B was born, A's age was 20 - 5 = 15.

OA : B
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Re: "You were a quarter of my age when I was twice of your present age"  [#permalink]

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New post 11 Jan 2017, 10:38
1
Option B

Assume current age of B to be S years. -I
Given: When A was 2S years old, B was 2S/4 (=S/2) years old.

: B was S/2 years old, S/2 years ago (from -I)
: Hence, current age of A = 2S + S/2 years =5S/2 years

Given: 5 years from now -- A's age + B's age = 45
: (5S/2 + 5) + (S+5) = 45
: S = 10 : B's current age.
: A's current age = 5S/2 = 25.

Hence, A was 15 (25-10) years old when B was born.
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New post 15 Jan 2018, 08:34
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: "You were a quarter of my age when I was twice of your present age"   [#permalink] 15 Jan 2018, 08:34
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