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# Working together, John and Jack can type 20 pages in one hou

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Working together, John and Jack can type 20 pages in one hou [#permalink]

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09 Oct 2010, 01:26
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Difficulty:

25% (medium)

Question Stats:

77% (02:47) correct 23% (02:51) wrong based on 404 sessions

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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
[Reveal] Spoiler: OA
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Re: Hours to type pages [#permalink]

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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
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Re: Hours to type pages [#permalink]

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09 Oct 2010, 01:50
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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

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Re: Hours to type pages [#permalink]

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09 Oct 2010, 01:51
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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) --> $$x+1.25y-(x+y)=22-20$$ --> $$0.25y=2$$ --> $$y=8$$ --> $$x=12$$ --> $$\frac{y}{x}=\frac{8}{12}=\frac{2}{3}$$.

OR: as by increasing the rate of Jack by 25% 2 more pages can be typed in one hour than we can directly write: $$0.25y=2$$ --> --> $$y=8$$ --> $$x=12$$ --> $$\frac{y}{x}=\frac{8}{12}=\frac{2}{3}$$.

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Re: Hours to type pages [#permalink]

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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
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Re: Hours to type pages [#permalink]

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01 Dec 2011, 05:14
x+y=20
4x+5y=88
x=8
y=12

==>D
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Re: Hours to type pages [#permalink]

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22 Dec 2011, 02:22
D is the answer. Quite an easy one.
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Re: Working together, John and Jack can type 20 pages in one hou [#permalink]

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07 Nov 2013, 10:17
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Re: Working together, John and Jack can type 20 pages in one hou [#permalink]

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01 Dec 2014, 10:56
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Re: Working together, John and Jack can type 20 pages in one hou [#permalink]

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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.

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

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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)

$$\frac{a+b}{a+1.25b} = \frac{10}{11}$$

$$\frac{b}{a} = \frac{2}{3}$$

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Working together, John and Jack can type 20 pages in one hou [#permalink]

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01 Apr 2015, 22:45
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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 :
$$\frac{8}{12} = \frac{2}{3}$$
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Re: Working together, John and Jack can type 20 pages in one hou [#permalink]

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

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

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