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percentage increase question

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percentage increase question

by redman » Mon Sep 29, 2008 5:31 am
this is a basic question that i'm trying to figure out.. its on a Kaplan guide book..

Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week, and works 10 percent fewer hours each week. Having an assistant increases Jane's output of toy bears per hour by what percent?

I answered 100 %, but the correct answer is 200%. Is this a trick question? What should I look out for in future questions to avoid this pitfall?

Any help is much appreciated.
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by GG04 » Mon Sep 29, 2008 5:49 am
I do not understand how to get 200% either. But this is my explanation for doing this.
Lets assume she makes 100 bears per week and works 10 hours.
So number of bears she makes in an hour = 100/10 = 10 bears/hour

With assistant, she makes 80% more = 180 bears per week and works 10% less = 9 hours per week.
So number of bears she makes with assistant in an hour = 180/9 =
20 bears/hour

Percent inc = inc/original * 100 = (20-10)/10 * 100 = 100%.
How do u get 200%?
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by hislander819 » Mon Sep 29, 2008 9:32 am
I am generally much stronger in Verbal, so whenever possible I will try to plug in values to arrive at my answer. Thus, see below:

Assume Jane works 40 hours per week, and has a weekly output of 120 bears.

Now, we need to calculate her weekly output with an assistant:

120 x .8 = 96 (then add it to 120 to get 80% more)
120 + 96 = 216

So, with an assistant she makes 216 bears per week. As for her hours, she works 10% less with an assistant. So:

40 x .10 = 4
40 - 4 = 36

Therefore, her output of toy bears went from 120/40 = 3/week to 216/36 = 6/week.

Then, its simply 6/3 = 2, or 200%
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percentage increase question

by raijonney » Mon Sep 29, 2008 10:29 pm
Lets say:

Jane makes x bears per week
and Jane works for y hours per week

therefore, she makes x bears in y hours (per week)
which implies she makes x/y bears per hour (per week)

Now with help of an assistant:

Jane makes 80% more bears are made i.e. x + 0.8x = 1.8x bears per week, and
works 10% less i.e. y - .1y = 0.9y hours per week

therefore, now together they make 1.8x/0.9y bears per hour (per week)

Hence % increase in output PER HOUR is :

((1.8x/0.9y) / (x/y) ) * 100 = 200 %
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by GG04 » Tue Sep 30, 2008 6:56 am
Raionney and hislander,

the problem with ur computation is that u have not considered the % increase which is (Increased value - original value)/original value
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by varun nagpal » Tue Sep 30, 2008 11:03 am
200% of 3 weeks is 9 weeks not 6 weeks (common sense)


Even I get 100% the question is worng or the answer given in Kapalan is worng
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by varun nagpal » Tue Sep 30, 2008 11:04 am
200% of 3 weeks is 9 weeks not 6 weeks (common sense)


Even I get 100% the question is worng or the answer given in Kapalan is worng
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by exeter » Tue Sep 30, 2008 4:44 pm
GG04 wrote:I do not understand how to get 200% either. But this is my explanation for doing this.
Lets assume she makes 100 bears per week and works 10 hours.
So number of bears she makes in an hour = 100/10 = 10 bears/hour

With assistant, she makes 80% more = 180 bears per week and works 10% less = 9 hours per week.
So number of bears she makes with assistant in an hour = 180/9 =
20 bears/hour

Percent inc = inc/original * 100 = (20-10)/10 * 100 = 100%.
How do u get 200%?
GG04 - your reasoning is perfect until the last sentence.
% increase = 100 * [ new rate ] / [old rate]
There is NO subtraction.

[new rate] = 20 bears / hour
[old rate] = 10 bears / hour

Therefore the % increase = 100* [ 20 bears / hour ] / [10 bears / hour] = 100 * [20 / 10] = 200%
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by GG04 » Tue Sep 30, 2008 5:48 pm
i am not sure if i am missing something here, but why wud u just multiply it by the new rate? is'nt that conceptually wrong?
increase in value of anything has to be the difference in new value and old value..
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by exeter » Tue Sep 30, 2008 6:34 pm
Ahh ok sorry. I interpreted the question to mean something else. I agree with you.

Question: “Having an assistant increases Jane's output of toy bears per hour by what percent?”

I interpreted the question as how fast Jane + assistant is working, compared with Jane alone. This is 200% as Jane + assistant is twice as fast as Jane solo (the multiplication of 100 was just to get it into % form, I am dividing the new rate by the old rate).

However looking at the question again, I realise it says by what % has Jane’s output increased. Which is what you did.

Based on the wording of the question, I think 100% is the right answer and Kaplan’s answer is wrong (or they worded the question wrongly).
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