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# A day is divided into 10 new-hours, each new-hour is divided

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A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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18 May 2013, 12:29
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95% (hard)

Question Stats:

44% (02:13) correct 56% (02:23) wrong based on 157 sessions

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A day is divided into 10 new-hours, each new-hour is divided into 100 new-minutes, and each new-minute is divided into 100 new-seconds. In terms of time elapsed, what is the ratio of a new-second to an ordinary second?

(A) $$\frac{3}{5}$$

(B) $$\frac{108}{125}$$

(C) 1

(D) $$\frac{125}{108}$$

(E) $$\frac{5}{3}$$
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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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18 May 2013, 16:07
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$$NewSecond=\frac{1}{10*100*100}$$ this means 1day/(Hours*Min*Sec)
$$OldSecond=\frac{1}{24*60*60}$$

$$\frac{NewS}{OldS}=\frac{24*60*60}{10*100*100}=\frac{108}{125}$$

B
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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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18 May 2013, 22:51
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JimmyChen wrote:
A day is divided into 10 new-hours, each new-hour is divided into 100 new-minutes, and each new-minute is divided into 100 new-seconds. In terms of time elapsed, what is the ratio of a new-second to an ordinary second?

(A) $$\frac{3}{5}$$

(B) $$\frac{108}{125}$$

(C) 1

(D) $$\frac{125}{108}$$

(E) $$\frac{5}{3}$$

Nice question... Got confused a little bit at the beginning

Number of seconds in an ordinary day = $$24 * 60 * 60$$

Number of seconds in the new day = $$10*100*100$$

Clearly new day has more number of seconds than the ordinary day.

So new second must take less time when compared to the ordinary one.

So the ration of new second to old second..... 24*60*60/10*100*100

Which is 108/125
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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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19 May 2013, 03:27
Zarrolou wrote:
$$NewSecond=\frac{1}{10*100*100}$$ this means 1day/(Hours*Min*Sec)
$$OldSecond=\frac{1}{24*60*60}$$

$$\frac{NewS}{OldS}=\frac{24*60*60}{10*100*100}=\frac{108}{125}$$

B

Hi Zarrolou,

my query is about the fraction 1/ 10*100*100. why are u taking fraction instead of 10*100*100?

kindly elaborate the concept.
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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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19 May 2013, 03:35
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atalpanditgmat wrote:

Hi Zarrolou,

my query is about the fraction 1/ 10*100*100. why are u taking fraction instead of 10*100*100?

kindly elaborate the concept.

You have to start from a common point: the day.
This then is divided differently by the two metods.

The new one has 10*100*100 seconds in one day, the old one has 24*60*60 seconds.
This means that the day is divided in 10*100*100 seconds in the new method, and in 24*60*60 seconds in the old method.

And here we get the fractions $$\frac{1}{10*100*100}$$ and $$\frac{1}{24*60*60}$$.
If you want the time elapsed you have to divide the day by the total number of seconds.

The number $$10*100*100$$ is the total number of seconds in a day, not the "time elapsed" in each one (as the queston asks)

Hope it's clear, let me know
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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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19 May 2013, 03:40
Zarrolou wrote:
atalpanditgmat wrote:

Hi Zarrolou,

my query is about the fraction 1/ 10*100*100. why are u taking fraction instead of 10*100*100?

kindly elaborate the concept.

You have to start from a common point: the day.
This then is divided differently by the two metods.

The new one has 10*100*100 seconds in one day, the old one has 24*60*60 seconds.
This means that the day is divided in 10*100*100 seconds in the new method, and in 24*60*60 seconds in the old method.

And here we get the fractions $$\frac{1}{10*100*100}$$ and $$\frac{1}{24*60*60}$$.
If you want the time elapsed you have to divide the day by the total number of seconds.

The number $$10*100*100$$ is the total number of seconds in a day, not the "time elapsed" in each one (as the queston asks)

Hope it's clear, let me know

Thank you, it is much clear now....
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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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19 May 2013, 04:10
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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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19 May 2013, 13:25
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Zarrolou is exactly right...

When I originally did this question, I overlooked the fact that we're comparing the time elapsed for one new-second vs. one ordinary second and not the number of new-seconds vs. the number of ordinary seconds in a day.

To get the time elapsed per second, you need to divide 1 day by the number of seconds in 1 day, hence the fractions in Zarrolou's solution.
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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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23 Jun 2014, 00:36
For a day (with old seconds)

60 Seconds = 1 Minute
60 Minutes = 1 Hr
24Hrs = 1 Day

1 Day = 24 * 60 * 60 Seconds

$$1 Second = \frac{1}{24*60*60}$$ ............... (1)

For a day (with new seconds)

100 new-seconds = 1 new-minute
100 new-minute = 1 new hour
10 new Hr = 1 Day

1 New Day = 10 * 100 * 100 New seconds

$$1 New second = \frac{1}{10*100*100}$$ ............ (2)

$$Ratio = \frac{(2)}{(1)} = \frac{1 New second}{1 Second}$$

$$= \frac{\frac{1}{10*100*100}}{\frac{1}{24*60*60}}$$

$$= \frac{24*60*60}{10*100*100}$$

$$= \frac{108}{125}$$

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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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23 Aug 2015, 05:00
JimmyChen wrote:
A day is divided into 10 new-hours, each new-hour is divided into 100 new-minutes, and each new-minute is divided into 100 new-seconds. In terms of time elapsed, what is the ratio of a new-second to an ordinary second?

(A) $$\frac{3}{5}$$

(B) $$\frac{108}{125}$$

(C) 1

(D) $$\frac{125}{108}$$

(E) $$\frac{5}{3}$$

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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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05 Apr 2018, 11:14
JimmyChen wrote:
A day is divided into 10 new-hours, each new-hour is divided into 100 new-minutes, and each new-minute is divided into 100 new-seconds. In terms of time elapsed, what is the ratio of a new-second to an ordinary second?

(A) $$\frac{3}{5}$$

(B) $$\frac{108}{125}$$

(C) 1

(D) $$\frac{125}{108}$$

(E) $$\frac{5}{3}$$

In an ordinary day, there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Thus in an ordinary day, there are 24 x 60 x 60 ordinary seconds.

In a new-day, there are 10 hours in a day, 100 minutes in an hour, and 100 seconds in a minute. Thus in a new-day, there are 10 x 100 x 100 new-seconds.

Since the time elapsed of a day (regardless it’s an ordinary day or a new-day) has to be the same, a new-second is 1/(10 x 100 x 100) of a day and an ordinary second is 1/(24 x 60 x 60) of a day. Thus, the ratio of a new-second to an ordinary second is:

[1/(10 x 100 x 100)]/[1/(24 x 60 x 60)]

(24 x 60 x 60)/(10 x 100 x 100)

(12 x 3 x 3)/(5 x 5 x 5)

108/125 .

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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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05 Apr 2018, 11:55
The key to this question is to start comparing from whats common between the newly constructed metrics to old metrics.
In that sense 1 day remains 1 day in both metrics so we start from there.
1 day = 24 hrs*60 min*60 sec1 (old metrics), 1day = 10 hrs*100min*100 sec2
now we need sec2/sec1 which can be calculated from above expressions.
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Re: A day is divided into 10 new-hours, each new-hour is divided  [#permalink]

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17 Jul 2019, 06:32
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Re: A day is divided into 10 new-hours, each new-hour is divided   [#permalink] 17 Jul 2019, 06:32
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