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# Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes

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Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes  [#permalink]

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15 May 2015, 02:26
6
00:00

Difficulty:

35% (medium)

Question Stats:

76% (02:23) correct 24% (03:06) wrong based on 170 sessions

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Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes his pace, so the remaining letters take him five additional hours to finish. Tom's rate during the first two hours is how many times his rate during the following five hours?

A. 10/21
B. 7/12
C. 14/15
D. 15/14
E. 12/7

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Joined: 04 Jan 2015
Posts: 2184
Re: Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes  [#permalink]

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15 May 2015, 03:51
Hi reto,

Presenting the detailed solution below:

Given
We are given work done by Tom in first 2 hours and the following 5 hours. We are asked to find the ratio of rates of work done by Tom in the first two hours to the following 5 hours.

Approach
We know that Work = Rate * Time. We know the amount of work done in the first 2 hours and amount of work done in the following 5 hours along with the time taken to do the work. We can use this to find out the ratio of rates.

Working Out
Work done by Tom during the first 2 hours = 30% of 210 letters = 63 letters
Time taken by Tom = 2 hours

Tom's rate during the first 2 hours = $$\frac{63}{2}$$....... (1)

Work done by Tom during the following 5 hours = 70% of 210 letters = 147letters
Time taken by Tom = 5 hours

Tom's rate during the following 5 hours = $$\frac{147}{5}$$....... (2)

Hence, the ratio of rates = $$\frac{63}{2} * \frac{5}{147} = \frac{15}{14}$$

Hope its clear

Regards
Harsh
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Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes  [#permalink]

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25 Jan 2017, 07:52
EgmatQuantExpert wrote:
Hi reto,

Presenting the detailed solution below:

Given
We are given work done by Tom in first 2 hours and the following 5 hours. We are asked to find the ratio of rates of work done by Tom in the first two hours to the following 5 hours.

Approach
We know that Work = Rate * Time. We know the amount of work done in the first 2 hours and amount of work done in the following 5 hours along with the time taken to do the work. We can use this to find out the ratio of rates.

Working Out
Work done by Tom during the first 2 hours = 30% of 210 letters = 63 letters
Time taken by Tom = 2 hours

Tom's rate during the first 2 hours = $$\frac{63}{2}$$....... (1)

Work done by Tom during the following 5 hours = 70% of 210 letters = 147letters
Time taken by Tom = 5 hours

Tom's rate during the following 5 hours = $$\frac{147}{5}$$....... (2)

Hence, the ratio of rates = $$\frac{63}{2} * \frac{5}{147} = \frac{15}{14}$$

Hope its clear

Regards
Harsh

One quicker way to reduce this fraction is to keep the number of letters in their non-reduced form:

$$\frac{(.3)(210)}{2}$$ * $$\frac{5}{(.7)(210)}$$, which you can very quickly reduce to 15/14.
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Joined: 22 May 2016
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Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes  [#permalink]

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27 Jul 2018, 20:41
1
reto wrote:
Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes his pace, so the remaining letters take him five additional hours to finish. Tom's rate during the first two hours is how many times his rate during the following five hours?

A. 10/21
B. 7/12
C. 14/15
D. 15/14
E. 12/7

Rates without the 210 letters

The number of letters is irrelevant. The work = 100% whether the number of letters is 210 or 21,000 or 21 million.

30% of the work is done in a 2-hour period; 70% of the work is done in a 5-hour period

Rate for the first 2 hours: $$\frac{.3}{2}$$

Rate for the next 5 hours: $$\frac{.7}{5}$$

Ratio of 2-hour rate to 5-hour rate:

$$\frac{(\frac{.3}{2})}{(\frac{.7}{5})}=(\frac{.3}{2}*\frac{5}{.7})=\frac{1.5}{1.4}=\frac{15}{14}$$

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Joined: 09 Mar 2016
Posts: 1062
Re: Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes  [#permalink]

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28 Jul 2018, 00:32
1
reto wrote:
Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes his pace, so the remaining letters take him five additional hours to finish. Tom's rate during the first two hours is how many times his rate during the following five hours?

A. 10/21
B. 7/12
C. 14/15
D. 15/14
E. 12/7

I solved it upside down

Let 30% be 210
Then 100% is 700 letters
Rate 1 = $$\frac{210}{2}$$ = 105
Rate 2 = remaining #of letters 700-210 =490) hence $$\frac{490}{5}$$
$$\frac{105}{1}$$* $$\frac{5}{490}$$ = $$\frac{105}{98}$$= $$\frac{15}{14}$$

YAY!
Re: Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes &nbs [#permalink] 28 Jul 2018, 00:32
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