age ratio

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sgr21: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Mon Oct 21, 2013 12:52 am

by sgr21 » Wed Mar 12, 2014 1:51 am

if the ages of steve and jack are currently in the ration 3:5.after six years their ages are in the ratio of 2:3.what will be jacks age after 4 years?

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Mar 12, 2014 5:13 am

S/J = 3/5

(S + 6)/(J + 6) = 2/3
= 3s + 18 = 2J + 12
= 3s = 2J - 6
= 3*3J/5 = 2J - 6
= 9J = 10J - 30
= J = 30
So, 30+4 = 34

R A H U L

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Mar 12, 2014 7:37 am

sgr21 wrote:If the ages of Steve and Jack are currently in the ratio of 3:5. After six years their ages are in the ratio of 2:3. What will be Jack's age after 4 years?

Let S = Steve's present age
Let J = Jack's present age

The ages of Steve and Jack are currently in the ratio of 3:5
So, we can write: S/J = 3/5
Cross multiply to get: 3J = 5S
Rearrange to get: 3J - 5S = 0

After six years...
This next piece of information deals with their ages 6 years in the FUTURE.
Before we can deal with this information, we must find expressions that represent these FUTURE ages.
If S = Steve's present age, then S + 6 = Steve's age in 6 years
If J = Jacks's present age, then J + 6 = Jacks's age in 6 years

...their ages are in the ratio of 2:3
So, we can write: (S + 6)/(J + 6) = 2/3
Cross multiply to get: 2(J + 6) = 3(S + 6)
Expand: 2J + 12 = 3S + 18
Rearrange to get: 2J - 3S = 6

We now have the following two equations:
3J - 5S = 0
2J - 3S = 6

To solve for J, we need to ELIMINATE the S terms. To do so, let's take the top equation and multiply both sides by 3. AND we'll take the bottom equation and multiply both sides by 5 to get:
9J - 15S = 0
10J - 15S = 30

At this point, we can SUBTRACT the bottom equation from the top equation to get:
-J = -30
So, J = 30
This means that Jack's PRESENT age is 30.

What will be Jack's age after 4 years?
Jack will be 34 years old in 4 years.

---------------------

If anyone is interested, we have a free video lesson on how to solve past/present/future ages questions: https://www.gmatprepnow.com/module/gmat- ... ems?id=908
Once you've watched that video, you can try answering this question: https://www.gmatprepnow.com/module/gmat- ... ems?id=909

Here are a few more questions to practice with:
- https://www.beatthegmat.com/mother-and-d ... 71014.html
- https://www.beatthegmat.com/equations-t269315.html
- https://www.beatthegmat.com/jack-and-bil ... 74426.html
- a little trickier: https://www.beatthegmat.com/ratio-help-t271009.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Mar 12, 2014 9:45 am

sgr21 wrote:if the ages of steve and jack are currently in the ration 3:5.after six years their ages are in the ratio of 2:3.what will be jacks age after 4 years?

Alternate approach:

Let S = Steve's age now and J = Jack's age now.

In 6 years, (S+6) : (J+6) = 2:3.
The new ratio -- 2:3 -- implies that S+6 is a multiple of 2.
Implication:
S+6 = even
S = even - 6 = even - even = EVEN.

Since S must be even, test EVEN options for S/J = 3/5:
S=6, J=10
S=12, J=20
S=18, J=30
S=24, J=40.

Determine which option will yield a 2:3 ratio after each age increases by 6 years:
12:16 = 3:4.
18:26 = 9:13.
24:36 = 2:3.
30:46 = 15:23.

The option in red yields the required ratio.
Thus:
S=18 and J=30, implying that in 4 years Jack will be 34.

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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 » Wed Mar 12, 2014 10:17 am

sgr21 wrote:if the ages of steve and jack are currently in the ration 3:5

Current ages are 3x and 5x respectively

sgr21 wrote:After six years their ages are in the ratio of 2:3

3x + 6 / 5x + 6 = 2 / 3

9x + 18 = 10x + 12

6 = x

So the Present Ages of Steve and Jack are 18 and 30 respectively.

After 4 years age of Jack will be 30+ 4 => 34 years.

Abhishek

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Mar 12, 2014 12:34 pm

Hi sgr21,

The responses to your questions emphasize various ways to do the algebra or to "brute force" the possibilities. Each of these approaches is worth knowing. You should keep in mind though that if this were a PS question, you would have 5 answers to work with. You COULD use those answers against the question to figure out which one "matched" all the information in the prompt.

If you ignore the answers, you'll be forced to "do math" on every question. Of the various ways to solve any GMAT question, the "math approach" is often the one that takes the longest. Part of dealing with the GMAT in an effective way is to know how to use the alternative approaches AND which is fastest.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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