Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 19 Sep 2010
Posts: 25

Working together, John and Jack can type 20 pages in one hou [#permalink]
Show Tags
09 Oct 2010, 01:26
11
This post was BOOKMARKED
Question Stats:
78% (02:47) correct
22% (02:47) wrong based on 429 sessions
HideShow timer Statistics
Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John? A. 1/3 B. 2/5 C. 1/2 D. 2/3 E. 3/5
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 19 Sep 2010
Posts: 25

Re: Hours to type pages [#permalink]
Show Tags
09 Oct 2010, 01:44
Here is the way I solve it using the formula RATE = JOB / TIME
Let x be the Job done by Jack in one hour and y the job done by Johon in one hour.
Working together, John and Jack can type 20 pages in one hour : x/1 + y/1 = 20/1
they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%: 5/4(x/1) + y/1 = 22/1
Thus x=8 ; y=12 x/y = 2/3



Retired Moderator
Joined: 02 Sep 2010
Posts: 803
Location: London

Re: Hours to type pages [#permalink]
Show Tags
09 Oct 2010, 01:50
3
This post received KUDOS
3
This post was BOOKMARKED
Barkatis wrote: how would you solve this one ?
Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?
1/3 2/5 1/2 2/3 3/5 Lets say John types x pages an hour and Jack types y pages an hour. We know that x+y=20 Jack increase speed by 25% means he will type 1.25y pages an hour. So we get x+1.25y=22 We need to know the ratio of Jack's speed to John's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x). Subtracting both : 0.25y=2 so y=8 ... so x=12 (y/x)=2/3 Answer is (D)
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 39754

Re: Hours to type pages [#permalink]
Show Tags
09 Oct 2010, 01:51
6
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
Barkatis wrote: how would you solve this one ?
Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?
1/3 2/5 1/2 2/3 3/5 Let the rate of John be \(x\) pages per hour and the rate of Jack \(y\) pages per hour. Then as we can sum the rates and \(rate*time=job\): \((x+y)*1=20\) > \(x+y=20\); "They would be able to type 22 pages in one hour if Jack increases his typing speed by 25%": \((x+1.25y)*1=22\) > \(x+1.25y=22\); Question: \(\frac{y}{x}=?\) Subtract (1) from (2) > \(x+1.25y(x+y)=2220\) > \(0.25y=2\) > \(y=8\) > \(x=12\) > \(\frac{y}{x}=\frac{8}{12}=\frac{2}{3}\). Answer: D. OR: as by increasing the rate of Jack by 25% 2 more pages can be typed in one hour than we can directly write: \(0.25y=2\) > > \(y=8\) > \(x=12\) > \(\frac{y}{x}=\frac{8}{12}=\frac{2}{3}\). Answer: D.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 632

Re: Hours to type pages [#permalink]
Show Tags
30 Nov 2011, 23:07
Let the rate of John be x pages per hour and the rate of Jack y pages per hour. so x + y = 20(i) After 25% increase by y x + 1.25y = 22(ii) Solving i and ii y = 8 x = 12 Ratio = 2/3 Ans. D
_________________
Collections: PSof OG solved by GC members: http://gmatclub.com/forum/collectionpswithsolutionfromgmatclub110005.html DS of OG solved by GC members: http://gmatclub.com/forum/collectiondswithsolutionfromgmatclub110004.html 100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmatprepproblemcollections114358.html Collections of work/rate problems with solutions http://gmatclub.com/forum/collectionsofworkrateproblemwithsolutions118919.html Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixtureproblemswithbestandeasysolutionsalltogether124644.html



Intern
Joined: 23 May 2010
Posts: 7

Re: Hours to type pages [#permalink]
Show Tags
01 Dec 2011, 05:14
x+y=20 4x+5y=88 x=8 y=12
==>D



Senior Manager
Joined: 12 Oct 2011
Posts: 262

Re: Hours to type pages [#permalink]
Show Tags
22 Dec 2011, 02:22
D is the answer. Quite an easy one.
_________________
Consider KUDOS if you feel the effort's worth it



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16029

Re: Working together, John and Jack can type 20 pages in one hou [#permalink]
Show Tags
07 Nov 2013, 10:17
Hello from the GMAT Club BumpBot! 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16029

Re: Working together, John and Jack can type 20 pages in one hou [#permalink]
Show Tags
01 Dec 2014, 10:56
Hello from the GMAT Club BumpBot! 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Current Student
Status: The Final Countdown
Joined: 07 Mar 2013
Posts: 296
Concentration: Technology, General Management
GPA: 3.84
WE: Information Technology (Computer Software)

Re: Working together, John and Jack can type 20 pages in one hou [#permalink]
Show Tags
01 Apr 2015, 12:02
@Bunuel,when do i take rate as 1/x and i/y and when to take it directly as x and y?I took the former and it became quite convoluted while taking the former.
Please help!!!



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Working together, John and Jack can type 20 pages in one hou [#permalink]
Show Tags
01 Apr 2015, 22:33
Let the Rate of John = a & Rate of Jack = b Let the combined time taken = t (a+b)t = 20 ............... (1) 25% increase in rate of Jack \(= \frac{125b}{100}\) \((a + \frac{125b}{100})t = 22\) ......... (2) \(\frac{a+b}{a+1.25b} = \frac{10}{11}\) \(\frac{b}{a} = \frac{2}{3}\) Answer = D
_________________
Kindly press "+1 Kudos" to appreciate



Director
Joined: 07 Aug 2011
Posts: 579
Concentration: International Business, Technology

Working together, John and Jack can type 20 pages in one hou [#permalink]
Show Tags
01 Apr 2015, 22:45
1
This post was BOOKMARKED
Barkatis wrote: Working together, John and Jack can type 20 pages in one hour. If they would be able to type 22 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?
A. 1/3 B. 2/5 C. 1/2 D. 2/3 E. 3/5 so we are told that Jack's 25% typing speed contributes 2 pages , 100% speed would contribute 8 pages in an hours. So JACK types 8 Pages and JOHN types 12 Pages in an hour time. Ratio of their speed : \(\frac{8}{12} = \frac{2}{3}\) Answer D
_________________
Thanks, Lucky
_______________________________________________________ Kindly press the to appreciate my post !!



Manager
Joined: 18 Dec 2014
Posts: 101

Re: Working together, John and Jack can type 20 pages in one hou [#permalink]
Show Tags
02 Apr 2015, 02:56
Jack + John = 20 per hour Jack increase 25% = 22 per hour 25% = 2 100% = 8 Jack 100% = 8 per hour
20  8 = 12 per hour
John = 12 per hour Jack = 8 per hour
8 / 12 = 2 / 3



Senior Manager
Joined: 15 Sep 2011
Posts: 361
Location: United States
WE: Corporate Finance (Manufacturing)

Re: Working together, John and Jack can type 20 pages in one hou [#permalink]
Show Tags
25 Jun 2015, 11:15
Signature VeritasPrepKarishma move: If 2 is 25% of a number, the number is 8 and therefore, the new ratio is 10:12 and the old ratio 8:12 = 2:3



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16029

Re: Working together, John and Jack can type 20 pages in one hou [#permalink]
Show Tags
31 Aug 2016, 07:31
Hello from the GMAT Club BumpBot! 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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Working together, John and Jack can type 20 pages in one hou
[#permalink]
31 Aug 2016, 07:31







