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# Jane makes toy bears. When she works with an assistant, she makes 80

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Re: Jane makes toy bears. When she works with an assistant, she makes 80 [#permalink]
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We can use fractional equivalents here to solve the problem

80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears
10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours

Now we come to productivity
Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour
Hence the productivity is double with the assistant i.e. the increase in productivity is 100%
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Re: Jane makes toy bears. When she works with an assistant, she makes 80 [#permalink]
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Condition 1: Jane working alone:

Let's say Jane works 50 hrs/ week and make 100 bears. [I took smart numbers foe easy calculations]

toys produces in 1 hr = $$\frac{100}{50}$$ = 2 ------------------- eq 1

Condition 2: Jane + Assistant working together:

Hrs worked Jane = 45 [10% less hrs worked]
Toys produced = 180 [80% more toys produced]

Toys produced in 1 hr = $$\frac{180}{45}$$ = 4 ------------------- eq 2

% change = $$\frac{{Change In Value}}{{Original Value }}$$ * 100

=> % change = $$\frac{{4-2}}{2}$$ * 100

=> 100%

Ans: C
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Re: Jane makes toy bears. When she works with an assistant, she makes 80 [#permalink]
I would assume numbers to do this question

If the number of toy bears, Jane makes in a week are 1000 and she has to work 10 hours to do it.
Since, she makes 80% more toy bears per week and works 10% less hours to do the work with the assistant's help
The number of toy bears will be 1800 and the number of hours worked are 9.

So, previously she made 100 bears per hour(1000/10) and now she makes 200 bears/hour (1800/9)
This is an increase of 100%(Option C)
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Re: Jane makes toy bears. When she works with an assistant, she makes 80 [#permalink]
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Bunuel wrote:
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?

A. 20%
B. 80%
C. 100%
D. 180%
E. 200%

Let Jane makes x bears in t hours
Per hour Jane makes x/t bears.

with assistant Jane makes (1+0.8) = 1.8 x bears in (1-0.1) = 0.9t hours
Per hour Jane makes 1.8x/0.9 t = 2x/t bears

So increase in Jane's output per hour = (2x/t - x/t) *100/(x/t) = 100%
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Re: Jane makes toy bears. When she works with an assistant, she makes 80 [#permalink]
Bunuel wrote:
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?

A. 20%
B. 80%
C. 100%
D. 180%
E. 200%

In actual GMAT we should solve it by taking numbers.
Lets say Jane makes 100 bears in 10 hours
So in 1 hour Jane makes 10 bears

With assistant, Jane makes 100x1.8 = 180 bears in 10x0.9 = 9 hours
So in 1 hours Jane makes 180/9 = 20 bears

Increase in Jane's output = (20-10)/10 = 100%
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Re: Jane makes toy bears. When she works with an assistant, she makes 80 [#permalink]
1
Kudos
Bunuel wrote:
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?

A. 20%
B. 80%
C. 100%
D. 180%
E. 200%

work = rate × time

Since “80 percent more” corresponds to a factor of 1.8, we have:

w_2 = 1.8w_1

r_2 × t_2 = 1.8 × r_1 × t_1

Since “10 percent fewer” corresponds to a factor of 0.9, we have:

r_2 × (0.9 × t_1) = 1.8 × r_1 × t_1

Thus,

r_2/r_1 = 1.8/0.9 = 2

Since a factor of 2 corresponds to “100% percent greater,” having an assistant increases Jane’s output per hour by 100%.

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Re: Jane makes toy bears. When she works with an assistant, she makes 80 [#permalink]
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Re: Jane makes toy bears. When she works with an assistant, she makes 80 [#permalink]
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