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John plans his day such that he spends 30% of his time for exercise

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John plans his day such that he spends 30% of his time for exercise [#permalink] New post   Updated on: 22 Mar 2019, 05:30
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John plans his day such that he spends 30% of his time for exercise, some of his time for family and 45% of his time for his work. On a certain day he spent 20% more time than he had planned for exercising. If he cannot change the duration of time planned for his work, what percentage of family time does he have to reduce? Assuming that these are the only three tasks he plans to do.


A. 6%
B. 19%
C. 20%
D. 24%
E. 80%
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D

Originally posted by btrg on 22 Mar 2019, 05:27.
Last edited by Bunuel on 22 Mar 2019, 05:30, edited 1 time in total.
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Re: John plans his day such that he spends 30% of his time for exercise [#permalink] New post   22 Mar 2019, 05:42
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btrg wrote:
John plans his day such that he spends 30% of his time for exercise, some of his time for family and 45% of his time for his work. On a certain day he spent 20% more time than he had planned for exercising. If he cannot change the duration of time planned for his work, what percentage of family time does he have to reduce? Assuming that these are the only three tasks he plans to do.


A. 6%
B. 19%
C. 20%
D. 24%
E. 80%


Out of 100 units of his time, he spends 30 units on exercise, 45 on work and 25 on family (if these 3 are the only tasks)

20% extra time on exercise means 6 extra units on exercise since 20% of 30 = 6 units.

He needs to spend the same time on work so these 6 units will come out of family time.

6/25 = 24%

Answer (D)
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Re: John plans his day such that he spends 30% of his time for exercise [#permalink] New post   22 Mar 2019, 05:56
IMO D

By product consistency rule ,
family time has to decrease by (100/120)*30
= 25%

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Re: John plans his day such that he spends 30% of his time for exercise [#permalink] New post   24 Mar 2019, 18:33
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btrg wrote:
John plans his day such that he spends 30% of his time for exercise, some of his time for family and 45% of his time for his work. On a certain day he spent 20% more time than he had planned for exercising. If he cannot change the duration of time planned for his work, what percentage of family time does he have to reduce? Assuming that these are the only three tasks he plans to do.


A. 6%
B. 19%
C. 20%
D. 24%
E. 80%


Normally John spends 30% of his time for exercise and 45% for work, so he spends 25% for his family. However, on a certain day he spent 20% more time on exercising, that is, he spent 30 x 1.2 = 36 percent on exercising and since he still spent 45% for work, he spent 19% for his family. So the time he spent for his family on that day is

(25 - 19)/25 x 100 = 6 x 4 = 24 percent less than he normally does.

Answer: D
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Re: John plans his day such that he spends 30% of his time for exercise [#permalink] New post   24 Mar 2019, 21:51
Hi Scott or Karishma,

I don’t understand the last step. Why do we need to divide 6 over 25x100?

Why isn’t the answer 6%? The question asks “what percentage of family time does he have to reduce?” He only spent 19% of family time so he had to reduce his time by 6%.

Can you please help me understand where I’m wrong? Thank you!

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Re: John plans his day such that he spends 30% of his time for exercise [#permalink] New post   25 Mar 2019, 05:23
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Because family time is 25% of total time. So the reduced time should be from that 25% only.

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Re: John plans his day such that he spends 30% of his time for exercise [#permalink] New post   26 Mar 2019, 01:55
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rebeccarathvon wrote:
Hi Scott or Karishma,

I don’t understand the last step. Why do we need to divide 6 over 25x100?

Why isn’t the answer 6%? The question asks “what percentage of family time does he have to reduce?” He only spent 19% of family time so he had to reduce his time by 6%.

Can you please help me understand where I’m wrong? Thank you!

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Say you scored 50% in a certain exam last year. This year you scored 40%. So your score went down by 10 percentage points.

But if you scored 50 last year and only 40 this year, the percentage decrease in your score is (10/50)*100 = 20%.

Similarly,

The family time was 25%. Now the family point is 19%. That is a drop of 6 percentage POINTS.

But he was spending 25 hrs with the family before. Now he is spending 19 hrs. So he had to reduce his family time by 6 hrs for 25 hrs he was spending before. What is this in percentage terms?

(6/25)*100 = 24%
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Re: John plans his day such that he spends 30% of his time for exercise [#permalink] New post   27 Mar 2019, 18:48
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Let’s assume this is a money problem. In this case, he would have originally spent $25 on his family, and then later he was able to spend only $19 on his family. So yes, he has spent $6 less on his family, but this means that the percent change of his expenditure is (19 - 25)/25 x 100% = -6/25 x 100%= -24%, which is a 24% decrease.

The reason that this problem is so confusing is that the original units are in percents (rather than dollars or hours or other unit). So you are actually required to calculate the percent change of two percents rather than the easier idea of calculating the percent change in dollars or hours.
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Re: John plans his day such that he spends 30% of his time for exercise [#permalink]
27 Mar 2019, 18:48
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